{"id":36561,"date":"2022-12-31T12:26:15","date_gmt":"2022-12-31T06:56:15","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=36561"},"modified":"2022-12-31T00:26:43","modified_gmt":"2022-12-30T18:56:43","slug":"big-ideas-math-algebra-1-answers-chapter-7","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-algebra-1-answers-chapter-7\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring"},"content":{"rendered":"<p>Download pdf Chapter 7 Polynomial Equations and Factoring <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-algebra-1-answers\/\"><strong>Big Ideas Math Algebra 1 Answers<\/strong><\/a> is available here. So, all the students who are worried to solve the Big Ideas Math Book Algebra 1 Ch 7 Polynomial Equations and Factoring can get them from here. Refer to our Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring to get the solutions in an explanative way and understand each and every concept.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring<\/h2>\n<p>All the questions seen in Big Ideas Math Book Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring are prepared by the math experts. The topics covered in BIM Algebra 1 Chapter 7 are Adding and Subtracting Polynomials, Multiplying Polynomials, Special Products of Polynomials, Solving Polynomial Equations in Factored Form, Factoring, etc. Tap the links who wish to practice and start solving the problems in different ways.<\/p>\n<ul>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Maintaining_Mathematical_Proficiency\">Polynomial Equations and Factoring Maintaining Mathematical Proficiency &#8211; Page 355\u00a0<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Mathematical_Practices\">Polynomial Equations and Factoring Mathematical Practices &#8211; Page 356<\/a><\/li>\n<li><a href=\"#Lesson_7.1_Adding_and_Subtracting_Polynomials\">Lesson 7.1 Adding and Subtracting Polynomials &#8211; Page (357 to 364)\u00a0<\/a><\/li>\n<li><a href=\"#Adding_and_Subtracting_Polynomials_7.1_Exercises\">Adding and Subtracting Polynomials 7.1 Exercises &#8211; Page (362 to 364)<\/a><\/li>\n<li><a href=\"#Lesson_7.2_Multiplying_Polynomials\">Lesson 7.2 Multiplying Polynomials &#8211; Page (365 to 370)<\/a><\/li>\n<li><a href=\"#Multiplying_Polynomials_7.2_Exercises\">Multiplying Polynomials 7.2 Exercises &#8211; Page (369 to 370)<\/a><\/li>\n<li><a href=\"#Lesson_7.3_Special_Products_of_Polynomials\">Lesson 7.3 Special Products of Polynomials &#8211; Page (371 to 376)<\/a><\/li>\n<li><a href=\"#Special_Products_of_Polynomials_7.3_Exercises\">Special Products of Polynomials 7.3 Exercises &#8211; Page (375 to 376)<\/a><\/li>\n<li><a href=\"#Lesson_7.4_Solving_Polynomial_Equations_in_Factored_Form\">Lesson 7.4 Solving Polynomial Equations in Factored Form &#8211; Page (377 to 382)<\/a><\/li>\n<li><a href=\"#Solving_Polynomial_Equations_in_Factored_Form_7.4_Exercises\">Solving Polynomial Equations in Factored Form 7.4 Exercises &#8211; Page (381 to 382)<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Study_Skills:_Preparing_for_a_Test\">Polynomial Equations and Factoring Study Skills: Preparing for a Test &#8211; Page 383<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_7.1\u20137.4_Quiz\">Polynomial Equations and Factoring 7.1\u20137.4 Quiz &#8211; Page 384<\/a><\/li>\n<li><a href=\"#Lesson_7.5_Factoring_x2_+_bx_+_c\">Lesson 7.5 Factoring x2 + bx + c &#8211; Page (385 to 390)<\/a><\/li>\n<li><a href=\"#Factoring_x2_+_bx_+_c_7.5_Exercises\">Factoring x2 + bx + c 7.5 Exercises &#8211; Page (389 to 390)<\/a><\/li>\n<li><a href=\"#Lesson_7.6_Factoring_ax2_+_bx_+_c\">Lesson 7.6 Factoring ax2 + bx + c &#8211; Page (391 to 396)<\/a><\/li>\n<li><a href=\"#Factoring_ax2_+_bx_+_c_7.6_Exercises\">Factoring ax2 + bx + c 7.6 Exercises &#8211; Page (395 to 396)<\/a><\/li>\n<li><a href=\"#Lesson_7.7_Factoring_Special_Products\">Lesson 7.7 Factoring Special Products &#8211; Page (397 to 402)<\/a><\/li>\n<li><a href=\"#Factoring_Special_Products_7.7_Exercises\">Factoring Special Products 7.7 Exercises &#8211; Page (401 to 402)<\/a><\/li>\n<li><a href=\"#Lesson_7.8_Factoring_Polynomials_Completely\">Lesson 7.8 Factoring Polynomials Completely &#8211; Page (403 to 408)<\/a><\/li>\n<li><a href=\"#Factoring_Polynomials_Completely_7.8_Exercises\">Factoring Polynomials Completely 7.8 Exercises &#8211; Page (407 to 408)<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Performance_Task:_The_View_Matters\">Polynomial Equations and Factoring Performance Task: The View Matters &#8211; Page 409<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Chapter_Review\">Polynomial Equations and Factoring Chapter Review &#8211; Page (410 to 412)<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Chapter_Test\">Polynomial Equations and Factoring Chapter Test &#8211; Page 413<\/a><\/li>\n<li><a href=\"#Polynomial_Equations_and_Factoring_Cumulative_Assessment\">Polynomial Equations and Factoring Cumulative Assessment &#8211; Page (414 to 415)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Maintaining_Mathematical_Proficiency\"><\/a>Polynomial Equations and Factoring Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n3x &#8211; 7 + 2x<br \/>\nAnswer: 5x &#8211; 7<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n3x &#8211; 7 + 2x<br \/>\n3x + 2x &#8211; 7<br \/>\n5x &#8211; 7<\/p>\n<p>Question 2.<br \/>\n4r + 6 &#8211; 9r &#8211; 1<br \/>\nAnswer: -5(r &#8211; 1)<\/p>\n<p>Explanation:<br \/>\n4r + 6 &#8211; 9r &#8211; 1<br \/>\n4r &#8211; 9r + 6 &#8211; 1 = -5r + 5 = -5(r &#8211; 1)<br \/>\n4r + 6 &#8211; 9r &#8211; 1 = -5(r &#8211; 1)<\/p>\n<p>Question 3.<br \/>\n-5t + 3 &#8211; t &#8211; 4 + 8t<br \/>\nAnswer: 2t &#8211; 1<\/p>\n<p>Explanation:<br \/>\n-5t + 3 &#8211; t &#8211; 4 + 8t<br \/>\n= -5t &#8211; t + 8t + 3 &#8211; 4<br \/>\n= 2t &#8211; 1<br \/>\nSo, -5t + 3 &#8211; t &#8211; 4 + 8t = 2t &#8211; 1<\/p>\n<p>Question 4.<br \/>\n3(s &#8211; 1) + 5<br \/>\nAnswer: 3s + 2<\/p>\n<p>Explanation:<br \/>\n3(s &#8211; 1) + 5<br \/>\n= 3s &#8211; 3 + 5<br \/>\n= 3s + 2<br \/>\nSo, 3(s &#8211; 1) + 5 = 3s + 2<\/p>\n<p>Question 5.<br \/>\n2m &#8211; 7(3 &#8211; m)<br \/>\nAnswer: 3(3m &#8211; 7)<\/p>\n<p>Explanation:<br \/>\n2m &#8211; 7(3 &#8211; m)<br \/>\n= 2m &#8211; 21 + 7m<br \/>\n= 2m + 7m &#8211; 21<br \/>\n= 9m &#8211; 21<br \/>\n= 3(3m &#8211; 7)<br \/>\n2m &#8211; 7(3 &#8211; m) = 3(3m &#8211; 7)<\/p>\n<p>Question 6.<br \/>\n4(h + 6) &#8211; (h &#8211; 2)<br \/>\nAnswer: 3h + 25<\/p>\n<p>Explanation:<br \/>\n4(h + 6) &#8211; (h &#8211; 2)<br \/>\n= 4h + 24 &#8211; h + 2<br \/>\n= 4h &#8211; 4 + 24 + 2<br \/>\n= 3h + 25<br \/>\nSo, 4(h + 6) &#8211; (h &#8211; 2) = 3h + 25<\/p>\n<p><strong>Find the greatest common factor.<\/strong><br \/>\nQuestion 7.<br \/>\n20, 36<br \/>\nAnswer: 4<\/p>\n<p>Explanation:<br \/>\nFactors of 20 = 1, 2, <strong>4<\/strong>, 5, 10 and 20.<br \/>\nFactors of 36 = 1, 2, 3, <strong>4<\/strong>, 6, 9, 12, 18 and 36.<br \/>\nThe GCF of 20 and 36 is 4.<\/p>\n<p>Question 8.<br \/>\n42, 63<br \/>\nAnswer: 21<\/p>\n<p>Explanation:<br \/>\nFactors of 42 = 1, 2, 3, 6, 7, 14, <strong>21<\/strong>, 42<br \/>\nFactors of 63 = 1, 3, 7, 9, <strong>21<\/strong>, 63<br \/>\nThe GCF of 42 and 63 is 21.<\/p>\n<p>Question 9.<br \/>\n54, 81<br \/>\nAnswer: 27<\/p>\n<p>Explanation:<br \/>\nFactors of 54 = 1, 2, 3, 6, 9, 18, <strong>27<\/strong>, 54<br \/>\nFactors of 81 = 1, 3, 9, <strong>27<\/strong>, 81<br \/>\nThe greatest common factor of 54 and 81 is 27.<\/p>\n<p>Question 10.<br \/>\n72, 84<br \/>\nAnswer: 12<\/p>\n<p>Explanation:<br \/>\nFactors of 72 = 1, 2, 3, 4, 6, 8, 9, <strong>12<\/strong>, 18, 24, 36, 72<br \/>\nFactors of 84 = 1, 2, 3, 4, 6, 7, <strong>12<\/strong>, 14, 21, 28, 42, 84<br \/>\nThe GCF of 72 and 84 is 12.<\/p>\n<p>Question 11.<br \/>\n28, 64<br \/>\nAnswer: 4<\/p>\n<p>Explanation:<br \/>\nFactors of 28 = 1, 2, <strong>4<\/strong>, 7, 14, 28<br \/>\nFactors of 64 = 1, 2, <strong>4<\/strong>, 8, 16, 32, 64<br \/>\nThe GCF of 28 and 64 is 4.<\/p>\n<p>Question 12.<br \/>\n30, 77<br \/>\nAnswer: 1<\/p>\n<p>Explanation:<br \/>\nFactors of 30 = <strong>1<\/strong>, 2, 3, 5, 6, 10, 15, 30<br \/>\nFactors of 77 = <strong>1<\/strong>, 7, 11, 77<br \/>\nThe GCF of 30 and 77 is 1.<\/p>\n<p>Question 13.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nIs it possible for two integers to have no common factors? Explain your reasoning.<br \/>\nAnswer: No. Even if both integers are prime, they still share the common factor of 1.<\/p>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Mathematical_Practices\"><\/a>Polynomial Equations and Factoring Mathematical Practices<\/h3>\n<p>Mathematically proficient students consider concrete models when solving a mathematics problem.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Write the algebraic expression modeled by the algebra tiles.<br \/>\nQuestion 1.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36563\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.1\" width=\"258\" height=\"70\" \/><br \/>\nAnswer:<br \/>\nx\u00b2 + x\u00b2 + x\u00b2 &#8211; x\u00b2 + 1<br \/>\n= 3x\u00b2 &#8211; x\u00b2 + 1<br \/>\n= 2x\u00b2 + 1<\/p>\n<p>Question 2.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36564\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.2\" width=\"101\" height=\"69\" \/><br \/>\nAnswer: x &#8211; x\u00b2 = x(1 &#8211; x)<\/p>\n<p>Question 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36565\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.3\" width=\"141\" height=\"69\" \/><br \/>\nAnswer:<br \/>\n-x\u00b2 &#8211; x &#8211; x<br \/>\n= -x\u00b2 &#8211; 2x<br \/>\n= -x(x + 2)<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36566\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.4\" width=\"137\" height=\"72\" \/><br \/>\nAnswer:<br \/>\nx + x\u00b2 &#8211; 1<br \/>\nx\u00b2 + x &#8211; 1<\/p>\n<p>Question 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36567\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.5\" width=\"118\" height=\"72\" \/><br \/>\nAnswer:<br \/>\nx\u00b2 + 1 + 1<br \/>\n= x\u00b2 + 2<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36568\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.6\" width=\"132\" height=\"66\" \/><br \/>\nAnswer:<br \/>\nx &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1<br \/>\nx &#8211; 6<\/p>\n<p>Question 7.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36569\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.7\" width=\"132\" height=\"78\" \/><br \/>\nAnswer:<br \/>\n-x\u00b2 + x + x<br \/>\n-x\u00b2 + 2x<br \/>\nx(-x + 2)<br \/>\nx(2 &#8211; x)<\/p>\n<p>Question 8.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36570\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.8\" width=\"152\" height=\"61\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.8.png 152w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.8-150x61.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nAnswer: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9<\/p>\n<p>Question 9.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36571\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-1.9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 1.9\" width=\"134\" height=\"73\" \/><br \/>\nAnswer: x\u00b2 + x\u00b2 = 2x\u00b2<\/p>\n<h3><a id=\"Lesson_7.1_Adding_and_Subtracting_Polynomials\"><\/a>Lesson 7.1 Adding and Subtracting Polynomials<\/h3>\n<p><strong>Essential Question<\/strong> How can you add and subtract polynomials?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Adding Polynomials<br \/>\nWork with a partner. Write the expression modeled by the algebra tiles in each step.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36572\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 1\" width=\"517\" height=\"282\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-1.png 517w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-1-300x164.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><br \/>\nAnswer:<br \/>\nStep 1: x + x + x + 1 + 1 + x &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 = (3x + 2) + (x &#8211; 5)<br \/>\nStep 2: x + x + x + x + 1 + 1\u00a0 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1<br \/>\nStep 3: x + x + x + x + 1 + 1 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1 &#8211; 1<br \/>\nStep 4: 4x &#8211; 3<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Subtracting Polynomials<br \/>\nWork with a partner. Write the expression modeled by the algebra tiles in each step.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36573\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 2\" width=\"518\" height=\"348\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-2.png 518w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-2-300x202.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><br \/>\nAnswer:<br \/>\nStep 1: x\u00b2 + x + x + 1 + 1 &#8211; x &#8211; 1<br \/>\n= (x\u00b2 + 2x + 2) &#8211; (x &#8211; 1)<br \/>\nStep 2: x\u00b2 + x + x + 1 + 1 + (-1 + 1)<br \/>\nx\u00b2 + 2x + 2<br \/>\nStep 3: x\u00b2 + x + x &#8211; 1 + 1 + 1 + 1<br \/>\nx\u00b2 + 2x + 2<br \/>\nStep 4: x\u00b2 + x + (x &#8211; x) + 1 + 1 + 1<br \/>\nx\u00b2 + x + 3<br \/>\nStep 5: x\u00b2 + x + 1 + 1 + 1<br \/>\nx\u00b2 + x + 3<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you add and subtract polynomials?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36574\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 3\" width=\"229\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<ul>\n<li>Your first step is to change the subtraction problem to an addition problem.<\/li>\n<li>Then you add, just as you did in the adding polynomials lesson.<\/li>\n<\/ul>\n<p>Question 4.<br \/>\nUse your methods in Question 3 to find each sum or difference.<br \/>\na. (x<sup>2<\/sup> + 2x &#8211; 1) + (2x<sup>2<\/sup> &#8211; 2x + 1)<br \/>\nb. (4x + 3) + (x &#8211; 2)<br \/>\nc. (x<sup>2<\/sup> + 2) &#8211; (3x<sup>2<\/sup> + 2x + 5)<br \/>\nd. (2x &#8211; 3x) &#8211; (x<sup>2<\/sup> &#8211; 2x + 4)<br \/>\nAnswer:<br \/>\na. (x<sup>2<\/sup> + 2x &#8211; 1) + (2x<sup>2<\/sup> &#8211; 2x + 1)<br \/>\n(x<sup>2<\/sup> + 2x &#8211; 1) + (2x<sup>2<\/sup> &#8211; 2x + 1)<br \/>\nx\u00b2 + 2x\u00b2 + 2x &#8211; 2x &#8211; 1 + 1<br \/>\n3x\u00b2<br \/>\n(x<sup>2<\/sup> + 2x &#8211; 1) + (2x<sup>2<\/sup> &#8211; 2x + 1) = 3x\u00b2<\/p>\n<p>b. (4x + 3) + (x &#8211; 2)<br \/>\n(4x + 3) + (x &#8211; 2)<br \/>\n4x + x + 3 &#8211; 2<br \/>\n5x + 1<\/p>\n<p>c. (x<sup>2<\/sup> + 2) &#8211; (3x<sup>2<\/sup> + 2x + 5)<br \/>\n(x<sup>2<\/sup> + 2) &#8211; (3x<sup>2<\/sup> + 2x + 5)<br \/>\nx\u00b2 &#8211; 3x\u00b2 &#8211; 2x + 2 &#8211; 5<br \/>\n-2x\u00b2 &#8211; 2x &#8211; 3<br \/>\n-(2x\u00b2 + 2x + 3)<\/p>\n<p>d. (2x &#8211; 3x) &#8211; (x<sup>2<\/sup> &#8211; 2x + 4)<br \/>\n(2x &#8211; 3x) &#8211; (x<sup>2<\/sup> &#8211; 2x + 4)<br \/>\n-x &#8211; x\u00b2 + 2x &#8211; 4<br \/>\n-x\u00b2 + x &#8211; 4<br \/>\n-(x\u00b2 &#8211; x + 4)<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Find the degree of the monomial.<\/strong><br \/>\nQuestion 1.<br \/>\n-3x<sup>4<\/sup><br \/>\nAnswer:<br \/>\n-3x<sup>4 <\/sup><br \/>\nThe degree of a monomial is the sum of the exponents of the variables.<br \/>\nThe degree of the monomial is 4.<\/p>\n<p>Question 2.<br \/>\n7c<sup>3<\/sup>d<sup>2<\/sup><br \/>\nAnswer:<br \/>\n7c<sup>3<\/sup>d<sup>2<\/sup><br \/>\nThe degree of c is 3<br \/>\nThe degree of d is 2<br \/>\nThe degree of the monomial = 3 + 2 = 5<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{5}{3}\\)y<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{3}\\)y<br \/>\nThe degree of the monomial is 1.<\/p>\n<p>Question 4.<br \/>\n-20.5<br \/>\nAnswer:<br \/>\n-20.5<br \/>\n-20.5 is the same as -20.5x<sup>0<\/sup> since anything to the zero power is equal to 1.<\/p>\n<p><strong>Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.<\/strong><br \/>\nQuestion 5.<br \/>\n4 &#8211; 9z<br \/>\nAnswer:<br \/>\n4 &#8211; 9z<br \/>\nThe highest exponent in the polynomial is called a degree.<br \/>\nThe degree is 1.<br \/>\nThe coefficient is 9.<br \/>\nThere are two terms in the given polynomial.<\/p>\n<p>Question 6.<br \/>\nt<sup>2<\/sup> &#8211; t<sup>2<\/sup> &#8211; 10t<br \/>\nAnswer:<br \/>\nt<sup>2<\/sup> &#8211; t<sup>2<\/sup> &#8211; 10t<br \/>\nThe highest exponent in the polynomial is called a degree.<br \/>\nThe degree is 2.<br \/>\nThe coefficient is 10 and 1.<br \/>\nThere are three terms in the given polynomial.<\/p>\n<p>Question 7.<br \/>\n2.8x + x<sup>3<\/sup><br \/>\nAnswer:<br \/>\nThe highest exponent in the polynomial is called a degree.<br \/>\nThe degree is 3.<br \/>\nThe coefficient is 2.8 and 1.<br \/>\nThere are two terms in the given polynomial.<\/p>\n<p><strong>Find the sum or difference.<\/strong><br \/>\nQuestion 8.<br \/>\n(b &#8211; 10) + (4b &#8211; 3)<br \/>\nAnswer:<br \/>\n(b &#8211; 10) + (4b &#8211; 3)<br \/>\nb &#8211; 10 + 4b &#8211; 3<br \/>\n3b &#8211; 13<br \/>\n(b &#8211; 10) + (4b &#8211; 3) = 3b &#8211; 13.<\/p>\n<p>Question 9.<br \/>\n(x<sup>2<\/sup> &#8211; x &#8211; 2) + (7x<sup>2<\/sup> &#8211; x)<br \/>\nAnswer:<br \/>\n(x<sup>2<\/sup> &#8211; x &#8211; 2) + (7x<sup>2<\/sup> &#8211; x)<br \/>\nx\u00b2 &#8211; x &#8211; 2 + 7x\u00b2 &#8211; x<br \/>\n8x\u00b2 &#8211; 2x &#8211; 2<\/p>\n<p>Question 10.<br \/>\n(p<sup>2<\/sup> + p + 3) &#8211; (-4p<sup>2<\/sup> &#8211; p + 3)<br \/>\nAnswer:<br \/>\n(p<sup>2<\/sup> + p + 3) &#8211; (-4p<sup>2<\/sup> &#8211; p + 3)<br \/>\np\u00b2 + p + 3 + 4p\u00b2 + p &#8211; 3<br \/>\n5p\u00b2 + 2p<\/p>\n<p>Question 11.<br \/>\n(-k + 5) &#8211; (3k<sup>2<\/sup> &#8211; 6)<br \/>\nAnswer:<br \/>\n(-k + 5) &#8211; (3k<sup>2<\/sup> &#8211; 6)<br \/>\n-k + 5 &#8211; 3k\u00b2 + 6<br \/>\n-3k\u00b2 &#8211; k + 11<\/p>\n<p>Question 12.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe polynomial -16t<sup>2<\/sup> &#8211; 25t + 200 represents the height of the penny after t seconds.<br \/>\na. Write a polynomial that represents the distance between the penny and the paintbrush after t seconds.<br \/>\nb. Interpret the coefficients of the polynomial in part (a).<br \/>\nAnswer: The coefficients of the polynomials are -16 and -25.<\/p>\n<h3><a id=\"Adding_and_Subtracting_Polynomials_7.1_Exercises\"><\/a>Adding and Subtracting Polynomials 7.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhen is a polynomial in one variable in standard form?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44147\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 1\" width=\"550\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-1.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-1-300x33.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a trinomial in one variable of degree 5 in standard form.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-122122\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-2Q.jpg\" alt=\"https:\/\/ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"422\" height=\"77\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-2Q.jpg 422w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-2Q-300x55.jpg 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow can you determine whether a set of numbers is closed under an operation?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44148\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 3\" width=\"553\" height=\"82\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-3.png 553w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-3-300x44.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36575\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 4\" width=\"486\" height=\"46\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-4.png 486w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-4-300x28.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122123\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-4Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"663\" height=\"78\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-4Q.jpg 910w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-4Q-300x35.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-4Q-768x90.jpg 768w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><\/p>\n<p><strong>In Exercises 5\u201312, find the degree of the monomial.<\/strong><br \/>\nQuestion 5.<br \/>\n4g<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44149\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 5\" width=\"555\" height=\"59\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-5.png 555w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-5-300x32.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 6.<br \/>\n23x<sup>4<\/sup><br \/>\nAnswer:<br \/>\nIn the monimial 23x<sup>4 <\/sup>the exponent of x is 4.<br \/>\nSo, the degree is 4.<\/p>\n<p>Question 7.<br \/>\n-1.75k<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44150\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 7\" width=\"515\" height=\"63\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-7.png 515w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-7-300x37.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 8.<br \/>\n&#8211;\\(\\frac{4}{9}\\)<br \/>\nAnswer:<br \/>\nThe degree of the monomial is 0<\/p>\n<p>Question 9.<br \/>\ns<sup>8<\/sup>t<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44151\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 9\" width=\"565\" height=\"63\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-9.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-9-300x33.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 10.<br \/>\n8m<sup>2<\/sup>n<sup>4<\/sup><br \/>\nAnswer:<br \/>\nGiven monomial is 8m<sup>2<\/sup>n<sup>4<\/sup><br \/>\nThe degree of the monomial is 2+4=6<\/p>\n<p>Question 11.<br \/>\n9xy<sup>3<\/sup>z<sup>7<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44152\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 11\" width=\"565\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-11.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-11-300x46.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 12.<br \/>\n-3q<sup>4<\/sup>rs<sup>6<\/sup><br \/>\nAnswer:<br \/>\nGiven monomial is -3q<sup>4<\/sup>rs<sup>6<\/sup><br \/>\nThe degree of the monomial is 4 +1+6=11<\/p>\n<p><strong>In Exercises 13\u201320, write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.<\/strong><br \/>\nQuestion 13.<br \/>\n6c<sup>2<\/sup> + 2c<sup>4<\/sup> &#8211; c<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44153\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 13\" width=\"580\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-13.png 580w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-13-300x85.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 14.<br \/>\n4w<sup>11<\/sup> &#8211; w<sup>12<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122124\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-14Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"735\" height=\"92\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-14Q.jpg 999w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-14Q-300x37.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-14Q-768x95.jpg 768w\" sizes=\"(max-width: 735px) 100vw, 735px\" \/><\/p>\n<p>Question 15.<br \/>\n7 + 3p<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44154\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 15\" width=\"622\" height=\"138\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-15.png 622w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-15-300x67.png 300w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/p>\n<p>Question 16.<br \/>\n8d &#8211; 2 &#8211; 4d<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122126\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-16Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"635\" height=\"84\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-16Q.jpg 1045w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-16Q-300x40.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-16Q-1024x135.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.1-16Q-768x101.jpg 768w\" sizes=\"(max-width: 635px) 100vw, 635px\" \/><\/p>\n<p>Question 17.<br \/>\n3t<sup>8<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44155\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 17\" width=\"491\" height=\"162\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-17.png 491w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-17-300x99.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 18.<br \/>\n5z + 2z<sup>3<\/sup> + 3z<sup>4<\/sup><br \/>\nAnswer:<br \/>\nThe polynomial 5z + 2z<sup>3<\/sup> + 3z<sup>4 <\/sup>is in standard form.<br \/>\nThe greatest degree of the polynomial is 4.<br \/>\nSo, the degree is 4.<br \/>\nThe leading coefficient is 3.<br \/>\nThe polynomial has 3 terms, so it is a trinomial.<\/p>\n<p>Question 19.<br \/>\n\u03c0r<sup>2<\/sup> &#8211; \\(\\frac{5}{7}\\)r<sup>8<\/sup> + 2r<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44156\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 19\" width=\"575\" height=\"180\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-19.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-19-300x94.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\sqrt{7}\\)n<sup>4<\/sup><br \/>\nAnswer:<br \/>\nThe given polynomial \\(\\sqrt{7}\\)n<sup>4<\/sup><sup>\u00a0<\/sup>is in standard form.<br \/>\nThe degree is 4.<br \/>\nThe coefficient is \\(\\sqrt{7}\\).<br \/>\nThe polynomial has 1 term, so it is a monomial.<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe expression \\(\\frac{4}{3}\\) \u03c0r<sup>3<\/sup> represents the volume of a sphere with radius r. Why is this expression a monomial? What is its degree?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36576\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 5\" width=\"167\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44157\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 21\" width=\"627\" height=\"119\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-21.png 627w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-21-300x57.png 300w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe amount of money you have after investing $400 for 8 years and $600 for 6 years at the same interest rate is represented by 400x<sup>8<\/sup> + 600x<sup>6<\/sup>, where x is the growth factor. Classify the polynomial by the number of terms. What is its degree?<br \/>\nAnswer:<br \/>\nThe polynomial 400x<sup>8<\/sup> + 600x<sup>6 <\/sup>has a degree 8 and is a binomial.<\/p>\n<p><strong>In Exercises 23\u201330, find the sum.<\/strong><br \/>\nQuestion 23.<br \/>\n(5y + 4) + (-2y + 6)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44158\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 23\" width=\"435\" height=\"102\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-23.png 435w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-23-300x70.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 24.<br \/>\n(-8x &#8211; 12) + (9x + 4)<br \/>\nAnswer:<br \/>\n(-8x &#8211; 12) + (9x + 4)<br \/>\n= -8x &#8211; 12 + 9x + 4<br \/>\n= -8x + 9x &#8211; 12 + 4<br \/>\n= x &#8211; 8<\/p>\n<p>Question 25.<br \/>\n(2n<sup>2<\/sup> &#8211; 5n &#8211; 6) + (-n<sup>2<\/sup> &#8211; 3n + 11)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44159\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 25\" width=\"399\" height=\"140\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-25.png 399w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-25-300x105.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 26.<br \/>\n(-3p<sup>3<\/sup> + 5p<sup>2<\/sup> &#8211; 2p) + (-p<sup>3<\/sup> &#8211; 8p<sup>2<\/sup> &#8211; 15p)<br \/>\nAnswer:<br \/>\n(-3p<sup>3<\/sup> + 5p<sup>2<\/sup> &#8211; 2p) + (-p<sup>3<\/sup> &#8211; 8p<sup>2<\/sup> &#8211; 15p)<br \/>\n= -3p\u00b3 + 5p\u00b2 &#8211; 2p &#8211; p\u00b3 &#8211; 8p\u00b2 &#8211; 15p<br \/>\n= -4p\u00b3 &#8211; 3p\u00b2 &#8211; 17p<\/p>\n<p>Question 27.<br \/>\n(3g<sup>2<\/sup> &#8211; g) + (3g<sup>2<\/sup> &#8211; 8g + 4)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44160\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 27\" width=\"317\" height=\"179\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-27.png 317w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-27-300x169.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Question 28.<br \/>\n(9r<sup>2<\/sup> + 4r &#8211; 7) + (3r<sup>2<\/sup> &#8211; 3r)<br \/>\nAnswer:<br \/>\n(9r<sup>2<\/sup> + 4r &#8211; 7) + (3r<sup>2<\/sup> &#8211; 3r)<br \/>\n= 9r\u00b2 + 4r &#8211; 7 + 3r\u00b2 &#8211; 3r<br \/>\n= 9r\u00b2 + 3r\u00b2 + 4r &#8211; 3r &#8211; 7<br \/>\n= 12r\u00b2 + r &#8211; 7<\/p>\n<p>Question 29.<br \/>\n(4a &#8211; a<sup>3<\/sup> &#8211; 3) + (2a<sup>3<\/sup> &#8211; 5a<sup>2<\/sup> + 8)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44161\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 29\" width=\"349\" height=\"137\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-29.png 349w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-29-300x118.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/p>\n<p>Question 30.<br \/>\n(s<sup>3<\/sup> &#8211; 2s &#8211; 9) + (2s<sup>2<\/sup> &#8211; 6s<sup>3<\/sup> + s)<br \/>\nAnswer:<br \/>\n(s<sup>3<\/sup> &#8211; 2s &#8211; 9) + (2s<sup>2<\/sup> &#8211; 6s<sup>3<\/sup> + s)<br \/>\ns\u00b3 &#8211; 2s &#8211; 9 + 2s\u00b2 &#8211; 6s\u00b3 + s<br \/>\ns\u00b3 &#8211; 6s\u00b3 + 2s\u00b2 &#8211; 2s + s &#8211; 9<br \/>\n-5s\u00b3 + 2s\u00b2 &#8211; s &#8211; 9<\/p>\n<p><strong>In Exercises 31\u201338, find the difference.<\/strong><br \/>\nQuestion 31.<br \/>\n(d &#8211; 9) &#8211; (3d &#8211; 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44162\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 31\" width=\"413\" height=\"98\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-31.png 413w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-31-300x71.png 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<p>Question 32.<br \/>\n(6x + 9) &#8211; (7x + 1)<br \/>\nAnswer:<br \/>\n(6x + 9) &#8211; (7x + 1)<br \/>\n6x + 9 &#8211; 7x &#8211; 1<br \/>\n6x &#8211; 7x + 9 &#8211; 1<br \/>\n-x + 8<\/p>\n<p>Question 33.<br \/>\n(y<sup>2<\/sup> &#8211; 4y + 9) &#8211; (3y<sup>2<\/sup> &#8211; 6y &#8211; 9)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44163\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 33\" width=\"367\" height=\"141\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-33.png 367w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-33-300x115.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p>Question 34.<br \/>\n(4m<sup>2<\/sup> &#8211; m + 2) &#8211; (-3m<sup>2<\/sup> + 10m + 4)<br \/>\nAnswer:<br \/>\n(4m<sup>2<\/sup> &#8211; m + 2) &#8211; (-3m<sup>2<\/sup> + 10m + 4)<br \/>\n4m\u00b2 &#8211; m + 2 + 3m\u00b2 &#8211; 10m &#8211; 4<br \/>\n4m\u00b2 + 3m\u00b2 &#8211; m &#8211; 10m + 2 &#8211; 4<br \/>\n7m\u00b2 &#8211; 11m &#8211; 2<\/p>\n<p>Question 35.<br \/>\n(k<sup>3<\/sup> &#8211; 7k + 2) &#8211; (k<sup>2<\/sup> &#8211; 12)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44164\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 35\" width=\"512\" height=\"104\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-35.png 512w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-35-300x61.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 36.<br \/>\n(-r &#8211; 10) &#8211; (-4r<sup>3<\/sup> + r<sup>2<\/sup> + 7r)<br \/>\nAnswer:<br \/>\n(-r &#8211; 10) &#8211; (-4r<sup>3<\/sup> + r<sup>2<\/sup> + 7r)<br \/>\n-r &#8211; 10 + 4r\u00b3 &#8211; r\u00b2 &#8211; 7r<br \/>\n4r\u00b3 &#8211; r\u00b2 &#8211; 7r &#8211; r &#8211; 10<br \/>\n4r\u00b3 &#8211; r\u00b2 &#8211; 8r &#8211; 10<\/p>\n<p>Question 37.<br \/>\n(t<sup>4<\/sup> &#8211; t<sup>2<\/sup> + t) &#8211; (12 &#8211; 9t<sup>2<\/sup> &#8211; 7t)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44165\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 37\" width=\"449\" height=\"277\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-37.png 449w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-37-300x185.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>Question 38.<br \/>\n(4d &#8211; 6d<sup>3<\/sup> + 3d<sup>2<\/sup>) &#8211; (10d<sup>3<\/sup> + 7d &#8211; 2)<br \/>\nAnswer:<br \/>\n(4d &#8211; 6d<sup>3<\/sup> + 3d<sup>2<\/sup>) &#8211; (10d<sup>3<\/sup> + 7d &#8211; 2)<br \/>\n4d &#8211; 6d\u00b3 + 3d\u00b2 &#8211; 10d\u00b3 &#8211; 7d + 2<br \/>\n-16d\u00b3 + 3d\u00b2 &#8211; 3d + 2<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 39 and 40, describe and correct the error in finding the sum or difference.<br \/>\nQuestion 39.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36577\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 6\" width=\"352\" height=\"92\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-6.png 352w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-6-300x78.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44166\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 39\" width=\"562\" height=\"157\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-39.png 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-39-300x84.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 40.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36578\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 7\" width=\"330\" height=\"109\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-7.png 330w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-7-300x99.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n(x\u00b3 &#8211; 4x\u00b2 + 3) + (-3x\u00b3 + 8x &#8211; 2)<br \/>\nx\u00b3 &#8211; 3x\u00b3 &#8211; 4x\u00b2 + 8x + 3 &#8211; 2<br \/>\n-2x\u00b3 &#8211; 4x\u00b2 + 8x + 1<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe cost (in dollars)of making b bracelets is represented by 4 + 5b. The cost (in dollars) of making b necklaces is represented by 8b + 6. Write a polynomial that represents how much more it costs to make b necklaces than b bracelets.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36579\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 8\" width=\"274\" height=\"122\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44167\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 41\" width=\"577\" height=\"157\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-41.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-41-300x82.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe number of individual memberships at a fitness center in m months is represented by 142 + 12m. The number of family memberships at the fitness center in m months is represented by 52 + 6m. Write a polynomial that represents the total number of memberships at the fitness center.<br \/>\nAnswer:<br \/>\nThe number of individual memberships at a fitness center in m months is represented by 142 + 12m.<br \/>\nThe number of family memberships at the fitness center in m months is represented by 52 + 6m.<br \/>\n= 142 + 12m + 52 + 6m<br \/>\n= 18m + 194<br \/>\nThe total number of memberships at the fitness center is 18m + 194.<\/p>\n<p><strong>In Exercises 43\u201346, find the sum or difference.<\/strong><br \/>\nQuestion 43.<br \/>\n(2s<sup>2<\/sup> &#8211; 5st &#8211; t<sup>2<\/sup>) &#8211; (s<sup>2<\/sup> + 7st &#8211; t<sup>2<\/sup>)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44168\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 43\" width=\"377\" height=\"96\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-43.png 377w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-43-300x76.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/p>\n<p>Question 44.<br \/>\n(a<sup>2<\/sup> &#8211; 3ab + 2b<sup>2<\/sup>) + (-4a<sup>2<\/sup> + 5ab &#8211; b<sup>2<\/sup>)<br \/>\nAnswer:<br \/>\n(a<sup>2<\/sup> &#8211; 3ab + 2b<sup>2<\/sup>) + (-4a<sup>2<\/sup> + 5ab &#8211; b<sup>2<\/sup>)<br \/>\na<sup>2<\/sup> &#8211; 3ab + 2b<sup>2<\/sup>\u00a0-4a<sup>2<\/sup> + 5ab &#8211; b<sup>2<\/sup><br \/>\n-3a<sup>2<\/sup> + b<sup>2 <\/sup>+2ab<\/p>\n<p>Question 45.<br \/>\n(c<sup>2<\/sup> &#8211; 6d<sup>2<\/sup>) + (c<sup>2<\/sup> &#8211; 2cd + 2d<sup>2<\/sup>)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44169\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 45\" width=\"183\" height=\"99\" \/><\/p>\n<p>Question 46.<br \/>\n(-x<sup>2<\/sup> + 9xy) &#8211; (x<sup>2<\/sup> + 6xy &#8211; 8y<sup>2<\/sup>)<br \/>\nAnswer:<br \/>\n(-x<sup>2<\/sup> + 9xy) &#8211; (x<sup>2<\/sup> + 6xy &#8211; 8y<sup>2<\/sup>)<br \/>\n-x<sup>2<\/sup> + 9xy &#8211; x<sup>2<\/sup> &#8211; 6xy + 8y<sup>2<\/sup>)<br \/>\n-2x<sup>2<\/sup> + 3xy + 8y<sup>2<\/sup><\/p>\n<p><strong>REASONING<\/strong> In Exercises 47\u201350, complete the statement with always, sometimes, or never. Explain your reasoning.<br \/>\nQuestion 47.<br \/>\nThe terms of a polynomial are ________ monomials.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44170\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 47\" width=\"572\" height=\"88\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-47.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-47-300x46.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 48.<br \/>\nThe difference of two trinomials is _________ a trinomial.<br \/>\nAnswer: The difference of two trinomials is <span style=\"text-decoration: underline;\"><strong>sometimes<\/strong> <\/span>a trinomial.<\/p>\n<p>Question 49.<br \/>\nA binomial is ________ a polynomial of degree 2.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44171\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 49\" width=\"554\" height=\"62\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-49.png 554w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-49-300x34.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 50.<br \/>\nThe sum of two polynomials is _________ a polynomial.<br \/>\nAnswer: The sum of two polynomials is <span style=\"text-decoration: underline;\"><strong>always<\/strong> <\/span>a polynomial.<\/p>\n<p><strong>MODELING WITH MATHEMATICS<\/strong> The polynomial \u221216t<sup>2<\/sup> &#8211; v<sub>0<\/sub>t &#8211; s<sub>0<\/sub> represents the height (in feet) of an object, where v<sub>0<\/sub> is the initial vertical velocity (in feet per second), s<sub>0<\/sub> is the initial height of the object (in feet), and t is the time (in seconds). In Exercises 51 and 52, write a polynomial that represents the height of the object. Then \ue033 nd the height of the object after 1 second.<br \/>\nQuestion 51.<br \/>\nYou throw a water balloon from a building.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36580\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 9\" width=\"178\" height=\"199\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44172\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 51\" width=\"585\" height=\"297\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-51.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-51-300x152.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 52.<br \/>\nYou bounce a tennis ball on a racket.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36581\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 10\" width=\"158\" height=\"196\" \/><br \/>\nAnswer:<br \/>\nv0 = 16 ft\/sec<br \/>\ns0 = 3 ft<br \/>\n\u221216t<sup>2<\/sup> &#8211; v<sub>0<\/sub>t &#8211; s<sub>0<\/sub><br \/>\n-16t\u00b2 &#8211; 16t &#8211; 3<br \/>\n-16(1)\u00b2 &#8211; 16(1) &#8211; 3<br \/>\n-16 &#8211; 16 &#8211; 3<br \/>\n= -35 is less than 1.<\/p>\n<p>Question 53.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou drop a ball from a height of 98 feet. At the same time, your friend throws a ball upward. The polynomials represent the heights (in feet) of the balls after t seconds.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36582\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 11\" width=\"251\" height=\"216\" \/><br \/>\na. Write a polynomial that represents the distance between your ball and your friend\u2019s ball after t seconds.<br \/>\nb. Interpret the coefficients of the polynomial in part (a).<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44173\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 53\" width=\"559\" height=\"466\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-53.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-53-300x250.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nDuring a 7-year period, the amounts (in millions of dollars) spent each year on buying new vehicles N and used vehicles U by United States residents are modeled by the equations<br \/>\nN = -0.028t<sup>3<\/sup> + 0.06t<sup>2<\/sup>+ 0.1t + 17<br \/>\nU = -0.38t<sup>2<\/sup> + 1.5t + 42<br \/>\nwhere t = 1 represents the first year in the 7-year period.<br \/>\na. Write a polynomial that represents the total amount spent each year on buying new and used vehicles in the 7-year period.<br \/>\nAnswer:<br \/>\nN = -0.028t<sup>3<\/sup> + 0.06t<sup>2<\/sup>+ 0.1t + 17<br \/>\nU = -0.38t<sup>2<\/sup> + 1.5t + 42<br \/>\nS = N + U<br \/>\nS = -0.028t<sup>3<\/sup> + 0.06t<sup>2<\/sup>+ 0.1t + 17 + (-0.38t<sup>2<\/sup> + 1.5t + 42)<br \/>\nS = -0.028t<sup>3<\/sup> + 0.06t<sup>2<\/sup>+ 0.1t + 17 &#8211; 0.38t<sup>2<\/sup> + 1.5t + 42<br \/>\nS = -0.028t<sup>3<\/sup> &#8211; 0.32t<sup>2<\/sup> + 1.6t + 59<br \/>\nb. How much is spent on buying new and used vehicles in the fifth year?<br \/>\nAnswer:<br \/>\nS = -0.028t<sup>3<\/sup> &#8211; 0.32t<sup>2<\/sup> + 1.6t + 59<br \/>\nt = 5<br \/>\nS = -0.028(5)<sup>3<\/sup> &#8211; 0.32(5)<sup>2<\/sup> + 1.6(5) + 59<br \/>\nS = -3.5 &#8211; 8 + 8 + 59<br \/>\nS = $55.5<\/p>\n<p>Question 55.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nWrite the polynomial in standard form that represents the perimeter of the quadrilateral.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36583\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 12\" width=\"188\" height=\"99\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44174\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 55\" width=\"507\" height=\"163\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-55.png 507w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-55-300x96.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe right side of the equation of each line is a polynomial.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36584\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 13\" width=\"196\" height=\"180\" \/><br \/>\na. The absolute value of the difference of the two polynomials represents the vertical distance between points on the lines with the same x-value. Write this expression.<br \/>\nAnswer:<br \/>\n(x &#8211; 2) &#8211; (-2x + 1)<br \/>\n= x &#8211; 2 + 2x &#8211; 1<br \/>\n= 3x &#8211; 3<br \/>\n= 3(x &#8211; 1)<br \/>\nd = 3|x &#8211; 1|<br \/>\nb. When does the expression in part (a) equal 0? How does this value relate to the graph?<br \/>\nAnswer:<br \/>\nd = 3(x &#8211; 1)<br \/>\n3(x &#8211; 1) = 0<br \/>\nx &#8211; 1 = 0<br \/>\nx = 1<br \/>\nIt also represents the point of intersection of the two lines.<\/p>\n<p>Question 57.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that when adding polynomials, the order in which you add does not matter. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44175\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 57\" width=\"472\" height=\"57\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-57.png 472w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-57-300x36.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite two polynomials whose sum is x<sup>2<\/sup> and whose difference is 1.<br \/>\nAnswer:<br \/>\np(x) + q(x) = x\u00b2<br \/>\np(x) &#8211; q(x) = 1<br \/>\np(x) = ax\u00b2 + b<br \/>\nq(x) = cx\u00b2 + d<br \/>\np(x) + q(x) = (a + c)x\u00b2 + (b + d) = x\u00b2<br \/>\na + c = 1<br \/>\nb + d = 0<br \/>\np(x) &#8211; q(x) = (a &#8211; c)x\u00b2 + (b &#8211; d) = 1<br \/>\na &#8211; c = 0<br \/>\nb &#8211; d = 1<br \/>\nb = -d<br \/>\nb &#8211; d = 1<br \/>\nb + b = 1<br \/>\n2b = 1<br \/>\nb = 1\/2<br \/>\nd = -b = -1\/2<br \/>\na + c = 1<br \/>\na + a = 1<br \/>\n2a = 1<br \/>\na = 1\/2<br \/>\na = 1\/2 = c<br \/>\np(x) = 1\/2 x\u00b2 + 1\/2<br \/>\nq(x) = 1\/2 x\u00b2 &#8211; 1\/2<\/p>\n<p>Question 59.<br \/>\n<strong>REASONING<\/strong><br \/>\nDetermine whether the set is closed under the given operation. Explain.<br \/>\na. the set of negative integers; multiplication<br \/>\nb. the set of whole numbers; addition<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44176\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 59\" width=\"570\" height=\"147\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-59.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-59-300x77.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are building a multi-level deck.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36585\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 14\" width=\"302\" height=\"164\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-14.png 302w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-14-300x163.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\na. For each level, write a polynomial in standard form that represents the area of that level. Then write the polynomial in standard form that represents the total area of the deck.<br \/>\nAnswer:<br \/>\nA = x(10 + (x &#8211; 12))<br \/>\nA = 10x + x\u00b2 &#8211; 12x = x\u00b2 &#8211; 2x<br \/>\nLevel 2 is a rectangle having length x and breadth (x &#8211; 12)<br \/>\nA&#8217; = x(x &#8211; 12)<br \/>\nA&#8217; = x\u00b2 &#8211; 12x<br \/>\nx\u00b2 &#8211; 2x + x\u00b2 &#8211; 12x = 2x\u00b2 &#8211; 14x<br \/>\nb. What is the total area of the deck when x = 20?<br \/>\nAnswer:<br \/>\nA = 2x\u00b2 &#8211; 14x<br \/>\nx = 20<br \/>\nA = 2(20)\u00b2 &#8211; 14(20)<br \/>\nA = 800 &#8211; 280<br \/>\nA = 520<br \/>\nc. A gallon of deck sealant covers 400 square feet. How many gallons of sealant do you need to cover the deck in part (b) once? Explain.<br \/>\nAnswer:<br \/>\nA gallon of deck sealant covers 400 square feet.<br \/>\n400 sq. ft\/ 1 gallon = 520 sq.ft\/x gallons<br \/>\n400\/1 = 520\/x<br \/>\nx \u00d7 400 = 520<br \/>\nx = 520\/400<br \/>\nx = 1.3<\/p>\n<p>Question 61.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA hotel installs a new swimming pool and a new hot tub.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36586\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.1-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.1 15\" width=\"285\" height=\"167\" \/><br \/>\na. Write the polynomial in standard form that represents the area of the patio.<br \/>\nb. The patio will cost $10 per square foot. Determine the cost of the patio when x = 9.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44177\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 61\" width=\"587\" height=\"525\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-61.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-61-300x268.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 62.<br \/>\n2(x &#8211; 1) + 3(x + 2)<br \/>\nAnswer:<br \/>\n2(x &#8211; 1) + 3(x + 2)<br \/>\n2x &#8211; 2 + 3x + 6<br \/>\n2x + 3x &#8211; 2 + 6<br \/>\n5x + 4<\/p>\n<p>Question 63.<br \/>\n8(4y &#8211; 3) + 2(y &#8211; 5)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44178\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.1 Question 63\" width=\"494\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-63.png 494w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.1-Question-63-300x83.png 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p>Question 64.<br \/>\n5(2r + 1) &#8211; 3(-4r + 2)<br \/>\nAnswer:<br \/>\n5(2r + 1) &#8211; 3(-4r + 2)<br \/>\n10r + 5 + 12r &#8211; 6<br \/>\n10r + 12r + 5 &#8211; 6<br \/>\n22r &#8211; 1<\/p>\n<h3><a id=\"Lesson_7.2_Multiplying_Polynomials\"><\/a>Lesson 7.2 Multiplying Polynomials<\/h3>\n<p><strong>Essential Question<\/strong> How can you multiply two polynomials?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Multiplying Monomials Using Algebra Tiles<br \/>\nWork with a partner. Write each product. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36587\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 1\" width=\"470\" height=\"207\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-1.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-1-300x132.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-194646 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-1.png\" alt=\"Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-1\" width=\"563\" height=\"207\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Multiplying Binomials Using Algebra Tiles<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36588\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 2\" width=\"229\" height=\"218\" \/><br \/>\nWork with a partner. Write the product of two binomials modeled by each rectangular array of algebra tiles. In parts (c) and (d), first draw the rectangular array of algebra tiles that models each product.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36589\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 3\" width=\"516\" height=\"434\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-3.png 516w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-3-300x252.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Answer:<br \/>\na. (x + 3)(x &#8211; 2)<br \/>\nx(x &#8211; 2) + 3(x &#8211; 2)<br \/>\nx\u00b2 &#8211; 2x + 3x &#8211; 6<br \/>\nx\u00b2 + x &#8211; 6<br \/>\n(x + 3)(x &#8211; 2) = x\u00b2 + x &#8211; 6<br \/>\nb. (2x &#8211; 1)(2x + 1)<br \/>\n2x(2x + 1) &#8211; 1(2x + 1)<br \/>\n4x\u00b2 + 2x &#8211; 2x &#8211; 1<br \/>\n4x\u00b2 &#8211; 1<br \/>\n(2x &#8211; 1)(2x + 1) = 4x\u00b2 &#8211; 1<br \/>\nc. (x + 2)(2x &#8211; 1)<br \/>\nx(2x &#8211; 1) + 2(2x &#8211; 1)<br \/>\n2x\u00b2 &#8211; x + 4x &#8211; 2<br \/>\n2x\u00b2 + 3x &#8211; 2<br \/>\n(x + 2)(2x &#8211; 1) = 2x\u00b2 + 3x &#8211; 2<br \/>\nd. (-x &#8211; 2)(x &#8211; 3)<br \/>\n-x(x &#8211; 3) &#8211; 2(x &#8211; 3)<br \/>\n-x\u00b2 + 3x &#8211; 2x + 6<br \/>\n-x\u00b2 + x + 6<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you multiply two polynomials?<br \/>\nAnswer:<\/p>\n<ul>\n<li>First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.<\/li>\n<li>Add the powers of the same variables using the exponent rule.<\/li>\n<li>Simplify the resulting polynomial by adding or subtracting the like terms.<\/li>\n<\/ul>\n<p>Question 4.<br \/>\nGive another example of multiplying two binomials using algebra tiles that is similar to those in Exploration 2.<br \/>\nAnswer:<br \/>\nExample:<br \/>\n(x + 3)(x &#8211; 2)<br \/>\nx(x) + x(-2) + 3(x) + 3(-2)<br \/>\nx\u00b2 &#8211; 2x + 3x &#8211; 6<br \/>\nx\u00b2 + x &#8211; 6<br \/>\nExample 2:<br \/>\n(2x &#8211; 1)(2x + 1)<br \/>\n2x(2x) + 2x(1) &#8211; 1(2x) &#8211; 1(1)<br \/>\n4x\u00b2 + 2x &#8211; 2x &#8211; 1<br \/>\n4x\u00b2 &#8211; 1<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Use the Distributive Property to find the product.<\/strong><br \/>\nQuestion 1.<br \/>\n(y + 4)(y + 1)<br \/>\nAnswer: y\u00b2 + 5y + 4<\/p>\n<p>Explanation:<br \/>\n(y + 4)(y + 1)<br \/>\ny(y + 1) + 4(y + 1)<br \/>\ny\u00b2 + y + 4y + 4<br \/>\ny\u00b2 + 5y + 4<\/p>\n<p>Question 2.<br \/>\n(z &#8211; 2)(z + 6)<br \/>\nAnswer: z\u00b2 + 4z &#8211; 12<\/p>\n<p>Explanation:<br \/>\n(z &#8211; 2)(z + 6)<br \/>\nz(z + 6) &#8211; 2(z + 6)<br \/>\nz\u00b2 + 6z &#8211; 2z &#8211; 12<br \/>\nz\u00b2 + 4z &#8211; 12<\/p>\n<p><strong>Use a table to find the product.<\/strong><br \/>\nQuestion 3.<br \/>\n(p + 3)(p &#8211; 8)<br \/>\nAnswer: p\u00b2 &#8211; 5p &#8211; 24<\/p>\n<p>Explanation:<br \/>\n(p + 3)(p &#8211; 8) = p(p &#8211; 8) + 3(p &#8211; 8)<br \/>\n= p\u00b2 &#8211; 8p + 3p &#8211; 24<br \/>\n= p\u00b2 &#8211; 5p &#8211; 24<\/p>\n<p>Question 4.<br \/>\n(r &#8211; 5)(2r &#8211; 1)<br \/>\nAnswer: 2r\u00b2 &#8211; 11r + 5<\/p>\n<p>Explanation:<br \/>\n(r &#8211; 5)(2r &#8211; 1) = r(2r &#8211; 1) &#8211; 5(2r &#8211; 1)<br \/>\n= 2r\u00b2 &#8211; r &#8211; 10r + 5<br \/>\n= 2r\u00b2 &#8211; 11r + 5<\/p>\n<p><strong>Use the FOIL Method to find the product.<\/strong><br \/>\nQuestion 5.<br \/>\n(m \u2013 3)(m &#8211; 7)<br \/>\nAnswer: m\u00b2 &#8211; 10m + 21<\/p>\n<p>Explanation:<br \/>\n(m \u2013 3)(m &#8211; 7) = m(m) + m(-7) &#8211; 3(m) &#8211; 3(-7)<br \/>\n= m\u00b2 &#8211; 7m &#8211; 3m + 21<br \/>\n= m\u00b2 &#8211; 10m + 21<\/p>\n<p>Question 6.<br \/>\n(x &#8211; 4)(x + 2)<br \/>\nAnswer: x\u00b2 + 2x &#8211; 4x<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n(x &#8211; 4)(x + 2) = x(x + 2) -4(x + 2)<br \/>\n= x\u00b2 + 2x &#8211; 4x<\/p>\n<p>Question 7.<br \/>\n( 2u + \\(\\frac{1}{2}\\))( u \u2013 \\(\\frac{3}{2}\\))<br \/>\nAnswer: 2u\u00b2 + 3\\(\\frac{1}{2}\\)u &#8211; \\(\\frac{3}{4}\\)<\/p>\n<p>Explanation:<br \/>\n( 2u + \\(\\frac{1}{2}\\))( u \u2013 \\(\\frac{3}{2}\\)) = 2u(u) + 2u(\\(\\frac{3}{2}\\)) + \\(\\frac{1}{2}\\)(u) &#8211; (\\(\\frac{1}{2}\\))(\\(\\frac{3}{2}\\))<br \/>\n= 2u\u00b2 + 3u\u00a0 + \\(\\frac{1}{2}\\)u &#8211; \\(\\frac{3}{4}\\)<br \/>\n= 2u\u00b2 + 3\\(\\frac{1}{2}\\)u &#8211; \\(\\frac{3}{4}\\)<\/p>\n<p>Question 8.<br \/>\n(n + 2)(n<sup>2<\/sup> + 3)<br \/>\nAnswer: n\u00b3 + 2n\u00b2 + 3n + 6<\/p>\n<p>Explanation:<br \/>\n(n + 2)(n<sup>2<\/sup> + 3)<br \/>\n= n(n<sup>2<\/sup> + 3) + 2(n<sup>2<\/sup> + 3)<br \/>\n= n\u00b3 + 3n + 2n\u00b2 + 6<br \/>\n= n\u00b3 + 2n\u00b2 + 3n + 6<\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 9.<br \/>\n(x + 1)(x<sup>2<\/sup> + 5x + 8)<br \/>\nAnswer: x\u00b3 + 6x\u00b2 + 13x + 8<\/p>\n<p>Explanation:<br \/>\n(x + 1)(x<sup>2<\/sup> + 5x + 8)<br \/>\n= x(x<sup>2<\/sup> + 5x + 8) + 1(x<sup>2<\/sup> + 5x + 8)<br \/>\n= x\u00b3 + 5x\u00b2 + 8x + x\u00b2 + 5x + 8<br \/>\n= x\u00b3 + 6x\u00b2 + 13x + 8<\/p>\n<p>Question 10.<br \/>\n(n &#8211; 3)(n<sup>2<\/sup> &#8211; 2n + 4)<br \/>\nAnswer: n\u00b3 &#8211; 5n\u00b2 + 10n &#8211; 12<\/p>\n<p>Explanation:<br \/>\n(n &#8211; 3)(n<sup>2<\/sup> &#8211; 2n + 4)<br \/>\n= n(n<sup>2<\/sup> &#8211; 2n + 4) &#8211; 3(n<sup>2<\/sup> &#8211; 2n + 4)<br \/>\n= n\u00b3 &#8211; 2n\u00b2 + 4n &#8211; 3n\u00b2 + 6n &#8211; 12<br \/>\n= n\u00b3 &#8211; 5n\u00b2 + 10n &#8211; 12<\/p>\n<p>Question 11.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 5(a), how does the polynomial change when the longer base is extended by 1 foot? Explain.<br \/>\nAnswer:<br \/>\nArea of a trapezoid = 1\/2 \u00d7 h [b1 + b2]<br \/>\n= 1\/2 (x &#8211; 7)[x + (x + 11)]<br \/>\n= 1\/2 (x &#8211; 7)(2x + 11)<br \/>\n= 1\/2[x(2x + 11) + (-7)(2x + 11)]<br \/>\n= 1\/2(2x\u00b2 + 11x &#8211; 14x &#8211; 77)<br \/>\n= 1\/2(2x\u00b2 &#8211; 4x &#8211; 77)<\/p>\n<h3><a id=\"Multiplying_Polynomials_7.2_Exercises\"><\/a>Multiplying Polynomials 7.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nDescribe two ways to find the product of two binomials.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44179\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 1\" width=\"578\" height=\"144\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-1.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-1-300x75.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how the letters of the word FOIL can help you to remember how to multiply two binomials.<br \/>\nAnswer: The multiplication of polynomials using the FOIL method involves multiplying the first, outer, inner and last terms together and calculating the value.<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, use the Distributive Property to find the product.<\/strong><br \/>\nQuestion 3.<br \/>\n(x + 1)(x + 3)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44180\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 3\" width=\"408\" height=\"132\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-3.png 408w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-3-300x97.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 4.<br \/>\n(y + 6)(y + 4)<br \/>\nAnswer: y\u00b2 + 10y + 24<\/p>\n<p>Explanation:<br \/>\n(y + 6)(y + 4) = y(y + 4) + 6(y + 4)<br \/>\n= y\u00b2 + 4y + 6y + 24<br \/>\n= y\u00b2 + 10y + 24<br \/>\n(y + 6)(y + 4) = y\u00b2 + 10y + 24<\/p>\n<p>Question 5.<br \/>\n(z &#8211; 5)(z + 3)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44181\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 5\" width=\"406\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-5.png 406w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-5-300x100.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 6.<br \/>\n(a + 8)(a &#8211; 3)<br \/>\nAnswer: a\u00b2 + 5a &#8211; 24<\/p>\n<p>Explanation:<br \/>\n(a + 8)(a &#8211; 3) = a(a &#8211; 3) + 8(a &#8211; 3)<br \/>\n= a\u00b2 &#8211; 3a + 8a &#8211; 24<br \/>\n= a\u00b2 + 5a &#8211; 24<\/p>\n<p>Question 7.<br \/>\n(g &#8211; 7)(g &#8211; 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44182\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 7\" width=\"440\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-7.png 440w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-7-300x93.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Question 8.<br \/>\n(n &#8211; 6)(n &#8211; 4)<br \/>\nAnswer: n\u00b2 &#8211; 10n + 24<\/p>\n<p>Explanation:<br \/>\n(n &#8211; 6)(n &#8211; 4) = n(n &#8211; 4) &#8211; 6(n &#8211; 4)<br \/>\n= n\u00b2 &#8211; 4n &#8211; 6n + 24<br \/>\n= n\u00b2 &#8211; 10n + 24<\/p>\n<p>Question 9.<br \/>\n(3m + 1)(m + 9)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44183\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 9\" width=\"475\" height=\"131\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-9.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-9-300x83.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 10.<br \/>\n(5s + 6)(s &#8211; 2)<br \/>\nAnswer: 5s\u00b2 &#8211; 4s &#8211; 12<\/p>\n<p>Explanation:<br \/>\n(5s + 6)(s &#8211; 2) = 5s(s &#8211; 2) + 6(s &#8211; 2)<br \/>\n= 5s\u00b2 &#8211; 10s + 6s &#8211; 12<br \/>\n= 5s\u00b2 &#8211; 4s &#8211; 12<\/p>\n<p><strong>In Exercises 11\u201318, use a table to find the product.<\/strong><br \/>\nQuestion 11.<br \/>\n(x + 3)(x + 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44184\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 11\" width=\"318\" height=\"204\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-11.png 318w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-11-300x192.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Question 12.<br \/>\n(y + 10)(y &#8211; 5)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122128\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-12Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"328\" height=\"238\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-12Q.jpg 640w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-12Q-300x218.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 13.<br \/>\n(h &#8211; 8)(h &#8211; 9)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44185\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 13\" width=\"408\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-13.png 408w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-13-300x151.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 14.<br \/>\n(c &#8211; 6)(c &#8211; 5)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122129\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-14Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"393\" height=\"308\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-14Q.jpg 594w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-14Q-300x235.jpg 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><\/p>\n<p>Question 15.<br \/>\n(3k &#8211; 1)(4k + 9)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44186\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 15\" width=\"408\" height=\"209\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-15.png 408w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-15-300x154.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 16.<br \/>\n(5g + 3)(g + 8)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122130\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-16Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"343\" height=\"262\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-16Q.jpg 612w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-16Q-300x229.jpg 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>Question 17.<br \/>\n(-3 + 2j)(4j &#8211; 7)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44187\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 17\" width=\"454\" height=\"209\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-17.png 454w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-17-300x138.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 18.<br \/>\n(5d &#8211; 12)(-7 + 3d)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122131\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-18Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"526\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-18Q.jpg 745w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-18Q-300x111.jpg 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122132\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-18aQ.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"433\" height=\"99\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-18aQ.jpg 709w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-18aQ-300x69.jpg 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p><strong>ERRORANALYSIS<\/strong><br \/>\nIn Exercises 19 and 20, describe and correct the error in finding the product of the binomials.<br \/>\nQuestion 19.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36590\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 4\" width=\"315\" height=\"107\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-4.png 315w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-4-300x102.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44188\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 19\" width=\"473\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-19.png 473w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-19-300x105.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 20.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36591\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 5\" width=\"314\" height=\"148\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-5.png 314w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-5-300x141.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122133\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-19Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"297\" height=\"280\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-19Q.jpg 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/big-math-algebra-1.Chapter-7-Polynomial-Equations-and-Factoring-7.2-19Q-300x282.jpg 300w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<p><strong>In Exercises 21\u201330, use the FOIL Method to find the product.<\/strong><br \/>\nQuestion 21.<br \/>\n(b + 3)(b + 7)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44189\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 21\" width=\"419\" height=\"134\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-21.png 419w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-21-300x96.png 300w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Question 22.<br \/>\n(w + 9)(w + 6)<br \/>\nAnswer: w\u00b2 + 15w + 54<\/p>\n<p>Explanation:<br \/>\n(w + 9)(w + 6) = w(w) + w(9) + w(6) + 9(6)<br \/>\n= w\u00b2 + 9w + 6w + 54<br \/>\n= w\u00b2 + 15w + 54<\/p>\n<p>Question 23.<br \/>\n(k + 5)(k &#8211; 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44190\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 23\" width=\"454\" height=\"130\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-23.png 454w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-23-300x86.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 24.<br \/>\n(x &#8211; 4)(x + 8)<br \/>\nAnswer: x\u00b2 + 4x &#8211; 32<\/p>\n<p>Explanation:<br \/>\n(x &#8211; 4)(x + 8) = x(x) + x(-4) + x(8) + 8(-4)<br \/>\n= x\u00b2 &#8211; 4x + 8x &#8211; 32<br \/>\n= x\u00b2 + 4x &#8211; 32<\/p>\n<p>Question 25.<br \/>\n(q &#8211; \\(\\frac{3}{4}\\)) (q + \\(\\frac{1}{4}\\))<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44191\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 25\" width=\"506\" height=\"202\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-25.png 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-25-300x120.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Question 26.<br \/>\n(z &#8211; \\(\\frac{5}{3}\\)) (z &#8211; \\(\\frac{2}{3}\\))<br \/>\nAnswer: z\u00b2 + \\(\\frac{2}{3}\\)z &#8211; \\(\\frac{5}{3}\\)z + \\(\\frac{10}{9}\\)<\/p>\n<p>Explanation:<br \/>\n(z &#8211; \\(\\frac{5}{3}\\)) (z &#8211; \\(\\frac{2}{3}\\)) = z(z) + z(\\(\\frac{2}{3}\\)) &#8211; \\(\\frac{5}{3}\\)(z) + (-\\(\\frac{2}{3}\\))(-\\(\\frac{5}{3}\\))<br \/>\n= z\u00b2 + \\(\\frac{2}{3}\\)z &#8211; \\(\\frac{5}{3}\\)z + \\(\\frac{10}{9}\\)<\/p>\n<p>Question 27.<br \/>\n(9 &#8211; r)(2 &#8211; 3r)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 27\" width=\"551\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-27.png 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-27-300x90.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 28.<br \/>\n(8 &#8211; 4x)(2x + 6)<br \/>\nAnswer: 16x &#8211; 8x\u00b2 &#8211; 24x + 48<\/p>\n<p>Explanation:<br \/>\n(8 &#8211; 4x)(2x + 6) = 8(2x) &#8211; 4x(2x) &#8211; 4x(6) + 8(6)<br \/>\n= 16x &#8211; 8x\u00b2 &#8211; 24x + 48<\/p>\n<p>Question 29.<br \/>\n(w + 5)(w<sup>2<\/sup> + 3w)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 29\" width=\"523\" height=\"134\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-29.png 523w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-29-300x77.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p>Question 30.<br \/>\n(v &#8211; 3)(v<sup>2<\/sup> + 8v)<br \/>\nAnswer: v\u00b3 + 5v\u00b2 &#8211; 24v<\/p>\n<p>Explanation:<br \/>\n(v &#8211; 3)(v<sup>2<\/sup> + 8v) = v(v<sup>2<\/sup>) + v(8v) &#8211; 3(v<sup>2<\/sup>) &#8211; 3(8v)<br \/>\n= v\u00b3 + 8v\u00b2 &#8211; 3v\u00b2 &#8211; 24v<br \/>\n= v\u00b3 + 5v\u00b2 &#8211; 24v<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 31\u2013 34, write a polynomial that represents the area of the shaded region.<br \/>\nQuestion 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36592\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 6\" width=\"147\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 31\" width=\"517\" height=\"270\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-31.png 517w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-31-300x157.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36593\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 7\" width=\"151\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nlength = (p + 1)<br \/>\nwidth = 2p &#8211; 6<br \/>\nA = length \u00d7 width<br \/>\nA = (p + 1)(2p &#8211; 6)<br \/>\n= p(2p &#8211; 6) + 1(2p &#8211; 6)<br \/>\n= 2p\u00b2 &#8211; 6p + 2p &#8211; 6<br \/>\n= 2p\u00b2 &#8211; 4p &#8211; 6<\/p>\n<p>Question 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36594\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 8\" width=\"145\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 33\" width=\"587\" height=\"581\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-33.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-33-300x297.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36595\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 9\" width=\"153\" height=\"125\" \/><br \/>\nAnswer:<br \/>\nl = x &#8211; 7<br \/>\nw = 5<br \/>\nA = length \u00d7 width<br \/>\nArea of inner rectangle = 5(x &#8211; 7)<br \/>\n= 5x &#8211; 35<br \/>\nArea of square = s \u00d7 s<br \/>\nA = (x + 1)(x + 1)<br \/>\nA = x\u00b2 + 2x + 1<br \/>\nTotal = x\u00b2 + 2x + 1 &#8211; 5x + 35<br \/>\n= x\u00b2 &#8211; 3x + 36<\/p>\n<p><strong>In Exercises 35\u201342, find the product.<\/strong><br \/>\nQuestion 35.<br \/>\n(x + 4)(x<sup>2<\/sup> + 3x + 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44196\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 35\" width=\"215\" height=\"167\" \/><\/p>\n<p>Question 36.<br \/>\n(f + 1)(f<sup>2<\/sup> + 4f + 8)<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n(f + 1)(f<sup>2<\/sup> + 4f + 8)<br \/>\n(f<sup>2<\/sup> + 4f + 8)<br \/>\n<span style=\"text-decoration: underline;\">\u00d7 (f + 1)<\/span><br \/>\nf(f<sup>2<\/sup> + 4f + 8) + 1(f<sup>2<\/sup> + 4f + 8)<br \/>\nf\u00b3 + 4f\u00b2 + 8f + f\u00b2 + 4f + 8<br \/>\nf\u00b3 + 5f\u00b2 + 12f + 8<br \/>\nSo, (f + 1)(f<sup>2<\/sup> + 4f + 8) = f\u00b3 + 5f\u00b2 + 12f + 8<\/p>\n<p>Question 37.<br \/>\n(y + 3)( y<sup>2<\/sup> + 8y &#8211; 2)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 37\" width=\"228\" height=\"170\" \/><\/p>\n<p>Question 38.<br \/>\n(t &#8211; 2)(t<sup>2<\/sup> &#8211; 5t + 1)<br \/>\nAnswer:<br \/>\n(t<sup>2<\/sup> &#8211; 5t + 1)<br \/>\n<span style=\"text-decoration: underline;\">\u00d7 (t &#8211; 2)<\/span><br \/>\nt(t<sup>2<\/sup> &#8211; 5t + 1) &#8211; 2(t<sup>2<\/sup> &#8211; 5t + 1)<br \/>\n= t\u00b3 &#8211; 5t\u00b2 + t &#8211; 2t\u00b2 + 10t &#8211; 2<br \/>\n= t\u00b3 &#8211; 7t\u00b2 + 11t &#8211; 2<\/p>\n<p>Question 39.<br \/>\n(4 &#8211; b)(5b<sup>2<\/sup> + 5b &#8211; 4)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44198\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 39\" width=\"259\" height=\"170\" \/><\/p>\n<p>Question 40.<br \/>\n(d + 6)(2d<sup>2<\/sup> &#8211; d + 7)<br \/>\nAnswer:<br \/>\nGiven,<br \/>\n(d + 6)(2d<sup>2<\/sup> &#8211; d + 7)<br \/>\n(2d<sup>2<\/sup> &#8211; d + 7)<br \/>\n<span style=\"text-decoration: underline;\">\u00d7 (d + 6)<\/span><br \/>\n= d(2d<sup>2<\/sup> &#8211; d + 7) + 6(2d<sup>2<\/sup> &#8211; d + 7)<br \/>\n= 2d\u00b3 &#8211; d\u00b2 + 7d + 12d\u00b2 &#8211; 6d + 42<br \/>\n= 2d\u00b3 &#8211; d\u00b2 + 12d\u00b2 + 7d &#8211; 6d + 42<br \/>\n= 2d\u00b3 + 11 d\u00b2 + d + 42<\/p>\n<p>Question 41.<br \/>\n(3e<sup>2<\/sup> &#8211; 5e + 7)(6e + 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 41\" width=\"248\" height=\"167\" \/><\/p>\n<p>Question 42.<br \/>\n(6v<sup>2<\/sup> + 2v &#8211; 9)(4 &#8211; 5v)<br \/>\nAnswer: &#8211; 30v\u00b3 + 14v\u00b2 + 53v &#8211; 36<\/p>\n<p>Explanation:<br \/>\n(6v<sup>2<\/sup> + 2v &#8211; 9)(4 &#8211; 5v)<br \/>\n4(6v<sup>2<\/sup> + 2v &#8211; 9) &#8211; 5v(6v<sup>2<\/sup> + 2v &#8211; 9)<br \/>\n24v\u00b2 + 8v &#8211; 36 &#8211; 30v\u00b3 &#8211; 10v\u00b2 + 45v<br \/>\n&#8211; 30v\u00b3 + 14v\u00b2 + 53v &#8211; 36<\/p>\n<p>Question 43.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe football field is rectangular.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36596\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 10\" width=\"318\" height=\"132\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-10.png 318w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-10-300x125.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\na. Write a polynomial that represents the area of the football field.<br \/>\nb. Find the area of the football field when the width is 160 feet.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44200\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-43.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 43.1\" width=\"578\" height=\"461\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-43.1.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-43.1-300x239.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-43.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 43.2\" width=\"529\" height=\"206\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-43.2.png 529w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-43.2-300x117.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou design a frame to surround a rectangular photo. The width of the frame is the same on every side, as shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36597\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 11\" width=\"247\" height=\"188\" \/><br \/>\na. Write a polynomial that represents the combined area of the photo and the frame.<br \/>\nAnswer:<br \/>\nAnswer:<br \/>\nWidth = 2x inch<br \/>\nCombined length = 22 + 2x<br \/>\nCombined width = 20 + 2x<br \/>\nArea =\u00a0 length \u00d7 width<br \/>\nA = (22 + 2x)(20 + 2x)<br \/>\nA = 440 + 44x + 40x + 4x\u00b2<br \/>\nA = 4x\u00b2 + 84x + 440<\/p>\n<p>b. Find the combined area of the photo and the frame when the width of the frame is 4 inches.<br \/>\nAnswer:<br \/>\n2x = 4<br \/>\nx = 2<br \/>\nA = 4x\u00b2 + 84x + 440<br \/>\nx = 2<br \/>\nA = 4(2)\u00b2 + 84(2) + 440<br \/>\nA = 16 + 168 + 440<br \/>\nA = 624 sq. in<br \/>\nSo, the combined area is 624 sq. in.<\/p>\n<p>Question 45.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhen multiplying two binomials, explain how the degree of the product is related to the degree of each binomial.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44202\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 45\" width=\"546\" height=\"57\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-45.png 546w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-45-300x31.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite two polynomials that are not monomials whose product is a trinomial of degree 3.<br \/>\nAnswer:<br \/>\n(x\u00b2 &#8211; x)(x + 1)<br \/>\n= x\u00b2(x + 1) &#8211; x(x + 1)<br \/>\n= x\u00b2(x) + x\u00b2(1) &#8211; x(x) &#8211; x(1)<br \/>\n= x\u00b3 + x\u00b2 &#8211; x &#8211; 1<br \/>\nSo, this is trinomial has a degree 3.<\/p>\n<p>Question 47.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says the FOIL Method can be used to multiply two trinomials. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44203\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 47\" width=\"562\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-47.png 562w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-47-300x89.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe table shows one method of finding the product of two binomials.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36598\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 12\" width=\"181\" height=\"92\" \/><br \/>\na. Write the two binomials being multiplied.<br \/>\nAnswer:<br \/>\nThe first binomial is -4x + 3<br \/>\nThe second binomial is -8x &#8211; 9<\/p>\n<p>b. Determine whether a, b, c, and d will be positive or negative when x &gt; 0.<br \/>\nAnswer:<br \/>\nThe two binomials are -4x + 3 and -8x &#8211; 9<br \/>\na: (-4x)(-8x) is positive<br \/>\nb: (3)(-8x) is negative<br \/>\nc: (-4x)(-9) is positive<br \/>\nd: (3)(-9) is negative<br \/>\nHence, when x &gt;0<br \/>\na &#8211; positive<br \/>\nb &#8211; negative<br \/>\nc &#8211; positive<br \/>\nd &#8211; negative<\/p>\n<p>Question 49.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nYou use the Distributive Property to multiply (x + 3)(x &#8211; 5). Your friend uses the FOIL Method to multiply (x &#8211; 5)(x + 3). Should your answers be equivalent? Justify your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44204\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 49\" width=\"559\" height=\"88\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-49.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-49-300x47.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nThe shipping container is a rectangular prism. Write a polynomial that represents the volume of the container.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36599\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 13\" width=\"280\" height=\"145\" \/><br \/>\nAnswer:<br \/>\nl = (x + 1)<br \/>\nb = (4x &#8211; 3)<br \/>\nh = (x + 2)<br \/>\nwe know that,<br \/>\nV = lbh<br \/>\nV = (4x &#8211; 3)(x + 1)(x + 2)<br \/>\n= (4x &#8211; 3)(x\u00b2 + 2x + x + 2)<br \/>\n= (4x &#8211; 3)(x\u00b2 + 3x + 2)<br \/>\n= 4x\u00b3 + 12x\u00b2 + 8x &#8211; 3x\u00b2 &#8211; 9x &#8211; 6<br \/>\n= 4x\u00b3 + 9x\u00b2 &#8211; x &#8211; 6<br \/>\nV = 4x\u00b3 + 9x\u00b2 &#8211; x &#8211; 6<\/p>\n<p>Question 51.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nThe product of (x + m)(x + n) is x<sup>2<\/sup> + bx + c.<br \/>\na. What do you know about m and n when c &gt; 0?<br \/>\nb. What do you know about m and n when c &lt; 0?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44205\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 51\" width=\"580\" height=\"178\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-51.png 580w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-51-300x92.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write the absolute value function as a piecewise function.<\/strong><br \/>\nQuestion 52.<br \/>\ny = |x| + 4<br \/>\nAnswer:<br \/>\ny = x + 15 x &gt; 0<br \/>\ny = -x + 15 x &lt; 0<\/p>\n<p>Question 53.<br \/>\ny = 6|x &#8211; 3|<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44206\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 53\" width=\"425\" height=\"443\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-53.png 425w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-53-288x300.png 288w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 54.<br \/>\ny = -4|x + 2|<br \/>\nAnswer:<br \/>\ny = -4|x + 2|<br \/>\n-4(x+ 2)<br \/>\n= -4x &#8211; 8<br \/>\ny = -4(-(x + 2))<br \/>\ny = -4(-x &#8211; 2)<br \/>\ny = 4x + 8<\/p>\n<p><strong>Simplify the expression. Write your answer using only positive exponents.<\/strong><br \/>\nQuestion 55.<br \/>\n10<sup>2<\/sup> \u2022 10<sup>9<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44207\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 55\" width=\"175\" height=\"64\" \/><\/p>\n<p>Question 56.<br \/>\n\\(\\frac{x^{5} \\cdot x}{x^{8}}\\)<br \/>\nAnswer:<br \/>\n\\(\\frac{x^{5} \\cdot x}{x^{8}}\\)<br \/>\n= x<sup>6<\/sup>\/x<sup>8<\/sup><br \/>\n= 1\/x\u00b2<\/p>\n<p>Question 57.<br \/>\n(3z<sup>6<\/sup>)<sup>-3<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44208\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.2 Question 57\" width=\"407\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-57.png 407w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.2-Question-57-300x44.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 58.<br \/>\n\\(\\left(\\frac{2 y^{4}}{y^{3}}\\right)^{-2}\\)<br \/>\nAnswer:<br \/>\n\\(\\left(\\frac{2 y^{4}}{y^{3}}\\right)^{-2}\\)<br \/>\n(2y)<sup>-2<\/sup><br \/>\n= 1\/4y\u00b2<\/p>\n<h3><a id=\"Lesson_7.3_Special_Products_of_Polynomials\"><\/a>Lesson 7.3 Special Products of Polynomials<\/h3>\n<p><strong>Essential Question<\/strong> What are the patterns in the special products (a+ b)(a \u2013 b), (a + b)<sup>2<\/sup>, and (a \u2013 b)<sup>2<\/sup>?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding a Sum and Difference Pattern<br \/>\nWork with a partner. Write the product of two binomials modeled by each rectangular array of algebra tiles.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36600\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 1\" width=\"520\" height=\"246\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-1.png 520w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-1-300x142.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><br \/>\nAnswer:<br \/>\na. (x + 2)(x &#8211; 2) = x(x &#8211; 2) + 2(x &#8211; 2)<br \/>\n= x\u00b2 &#8211; 2x + 2x &#8211; 4<br \/>\n= x\u00b2 &#8211; 4<br \/>\nb. (2x &#8211; 1)(2x + 1)<br \/>\n= 2x(2x + 1) &#8211; 1(2x + 1)<br \/>\n= 4x\u00b2 + 2x &#8211; 2x &#8211; 1<br \/>\n= 4x\u00b2 &#8211; 1<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding the Square of a Binomial Pattern<br \/>\nWork with a partner. Draw the rectangular array of algebra tiles that models each product of two binomials. Write the product.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36601\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 2\" width=\"514\" height=\"246\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-2.png 514w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-2-300x144.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-194821 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-2.png\" alt=\"Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-2\" width=\"514\" height=\"246\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nWhat are the patterns in the special products (a + b)(a &#8211; b), (a + b)<sup>2<\/sup>, and (a &#8211; b)<sup>2<\/sup>?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36602\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 3\" width=\"225\" height=\"147\" \/><br \/>\nAnswer:<br \/>\n(a + b)(a &#8211; b)<br \/>\nApply distributive property<br \/>\na(a &#8211; b) + b(a &#8211; b)<br \/>\na\u00b2 &#8211; ab + ba &#8211; b\u00b2<br \/>\n(a + b)(a &#8211; b) = a\u00b2 &#8211; b\u00b2<br \/>\nSo, (a + b)(a &#8211; b) = a\u00b2 &#8211; b\u00b2<br \/>\n(a + b)(a + b)<br \/>\nApply distributive property<br \/>\na(a + b) + b(a + b)<br \/>\na\u00b2 + ab + ba + b\u00b2 = a\u00b2 + 2ab + b\u00b2<br \/>\n(a &#8211; b)(a &#8211; b)<br \/>\nApply distributive property<br \/>\na(a &#8211; b) &#8211; b(a &#8211; b)<br \/>\na\u00b2 &#8211; ab &#8211; ba + b\u00b2 = a\u00b2 &#8211; 2ab + b\u00b2<\/p>\n<p>Question 4.<br \/>\nUse the appropriate special product pattern to find each product. Check your answers using algebra tiles.<br \/>\na. (x + 3)(x &#8211; 3)<br \/>\nb. (x &#8211; 4)(x + 4)<br \/>\nc. (3x + 1)(3x &#8211; 1)<br \/>\nd. (x + 3)<sup>2<\/sup><br \/>\ne. (x &#8211; 2)<sup>2<\/sup><br \/>\nf. (3x + 1)<sup>2<\/sup><br \/>\nAnswer:<br \/>\na. (x + 3)(x &#8211; 3)<br \/>\nIt is in the form of (a + b)(a &#8211; b) = a\u00b2 &#8211; b\u00b2<br \/>\n(x + 3)(x &#8211; 3) = x\u00b2 &#8211; 3\u00b2<br \/>\n= x\u00b2 &#8211; 9<\/p>\n<p>b. (x &#8211; 4)(x + 4)<br \/>\nIt is in the form of (a + b)(a &#8211; b) = a\u00b2 &#8211; b\u00b2<br \/>\n(x &#8211; 4)(x + 4) = x\u00b2 &#8211; 4\u00b2<br \/>\n= x\u00b2 &#8211; 16<\/p>\n<p>c. (3x + 1)(3x &#8211; 1)<br \/>\nIt is in the form of (a + b)(a &#8211; b) = a\u00b2 &#8211; b\u00b2<br \/>\n(3x + 1)(3x &#8211; 1) = (3x)\u00b2 &#8211; 1<br \/>\n= 9x\u00b2 &#8211; 1<\/p>\n<p>d. (x + 3)\u00b2<br \/>\nIt is in the form of (a + b)<sup>2 <\/sup>= a\u00b2 + 2ab + b\u00b2<br \/>\n= (x)\u00b2 + (3)\u00b2 + 2(x)(3)<br \/>\n= x\u00b2 + 9 + 6x<\/p>\n<p>e. (x &#8211; 2)\u00b2<br \/>\nIt is in the form of (a &#8211; b)<sup>2 <\/sup>= a\u00b2 &#8211; 2ab + b\u00b2<br \/>\n(x &#8211; 2)\u00b2 = (x)\u00b2 + (2)\u00b2 + 2(x)(2)<br \/>\n= x\u00b2\u00a0 + 4 + 4x<\/p>\n<p>f. (3x + 1)\u00b2<br \/>\nIt is in the form of (a + b)<sup>2 <\/sup>= a\u00b2 + 2ab + b\u00b2<br \/>\n= (3x)\u00b2 + (1)\u00b2 + 2(3x)(1)<br \/>\n= 9x\u00b2 + 1 + 6x<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 1.<br \/>\n(x + 7)<sup>2<\/sup><br \/>\nAnswer: x\u00b2 + 49 + 14x<\/p>\n<p>Explanation:<br \/>\n(x + 7)\u00b2<br \/>\n(x + 7)\u00b2 = x\u00b2 + 7\u00b2 + 2(x)(7)<br \/>\n= x\u00b2 + 49 + 14x<br \/>\n(x + 7)\u00b2 = x\u00b2 + 49 + 14x<\/p>\n<p>Question 2.<br \/>\n(7x &#8211; 3)<sup>2<\/sup><br \/>\nAnswer: 49x\u00b2 &#8211; 42x + 9<\/p>\n<p>Explanation:<br \/>\n(7x &#8211; 3)\u00b2<br \/>\n(7x &#8211; 3)\u00b2 = (7x)\u00b2 + (3)\u00b2 &#8211; 2(7x)(3)<br \/>\n= 49x\u00b2 + 9 &#8211; 42x<br \/>\n= 49x\u00b2 &#8211; 42x + 9<\/p>\n<p>Question 3.<br \/>\n(4x &#8211; y)<sup>2<\/sup><br \/>\nAnswer: 16x\u00b2 + y\u00b2 &#8211; 8xy<\/p>\n<p>Explanation:<br \/>\n(4x &#8211; y)\u00b2<br \/>\n(4x &#8211; y)\u00b2 = (4x)\u00b2 + (y)\u00b2 &#8211; 2(4x)(y)<br \/>\n= 16x\u00b2 + y\u00b2 &#8211; 8xy<\/p>\n<p>Question 4.<br \/>\n(3m + n)<sup>2<\/sup><br \/>\nAnswer: 9m\u00b2 + n\u00b2 + 6mn<\/p>\n<p>Explanation:<br \/>\n(3m + n)\u00b2<br \/>\n(3m + n)\u00b2 = (3m)\u00b2 + (n)\u00b2 + 2(3m)(n)<br \/>\n= 9m\u00b2 + n\u00b2 + 6mn<\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 5.<br \/>\n(x + 10)(x &#8211; 10)<br \/>\nAnswer: x\u00b2 &#8211; 100<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n(x + 10)(x &#8211; 10)<br \/>\n(x + 10)(x &#8211; 10) = x\u00b2 &#8211; (10)\u00b2<br \/>\n= x\u00b2 &#8211; 100<\/p>\n<p>Question 6.<br \/>\n(2x + 1)(2x &#8211; 1)<br \/>\nAnswer: 4x\u00b2 &#8211; 1<\/p>\n<p>Explanation:<br \/>\n(2x + 1)(2x &#8211; 1)<br \/>\n(2x + 1)(2x &#8211; 1) = (2x)\u00b2 &#8211; (1)\u00b2<br \/>\n= 4x\u00b2 &#8211; 1<\/p>\n<p>Question 7.<br \/>\n(x + 3y)(x &#8211; 3y)<br \/>\nAnswer: x\u00b2 &#8211; 9y\u00b2<\/p>\n<p>Explanation:<br \/>\n(x + 3y)(x &#8211; 3y) = (x)\u00b2 &#8211; (3y)\u00b2<br \/>\n= x\u00b2 &#8211; 9y\u00b2<br \/>\n(x + 3y)(x &#8211; 3y) = x\u00b2 &#8211; 9y\u00b2<\/p>\n<p>Question 8.<br \/>\nDescribe how to use special product patterns to find 21<sup>2<\/sup>.<br \/>\nAnswer:<br \/>\n21\u00b2 = (20 + 1)\u00b2<br \/>\n(20 + 1)\u00b2 = (20)\u00b2 + (1)\u00b2 + 2(20)(1)<br \/>\n= 400 + 1 + 40<br \/>\n= 441<\/p>\n<p>Question 9.<br \/>\nEach of two dogs has one black gene (B) and one white gene (W). The Punnett square shows the possible gene combinations of an offspring and the resulting colors.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36603\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 4\" width=\"206\" height=\"206\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-4.png 206w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-4-150x150.png 150w\" sizes=\"(max-width: 206px) 100vw, 206px\" \/><br \/>\na. What percent of the possible gene combinations result in black?<br \/>\nAnswer:<br \/>\nEach of two dogs has one black gene (B) and one white gene (W). The Punnett square shows the possible gene combinations of an offspring and the resulting colors.<br \/>\n3\/4 = 75%<\/p>\n<p>b. Show how you could use a polynomial to model the possible gene combinations of the offspring.<br \/>\nAnswer:<br \/>\n0.5B + 0.5W<br \/>\nThere is an equivalent chance that the offspring receives a black or a white gene from each parent.<br \/>\n(0.5B + 0.5W)\u00b2<\/p>\n<h3><a id=\"Special_Products_of_Polynomials_7.3_Exercises\"><\/a>Special Products of Polynomials 7.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use the square of a binomial pattern.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44209\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 1\" width=\"559\" height=\"90\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-1.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-1-300x48.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36604\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 5\" width=\"506\" height=\"57\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-5.png 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-5-300x34.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\nAnswer: (x + 2)(x &#8211; 3) does not belong with the other three.<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, find the product.<\/strong><br \/>\nQuestion 3.<br \/>\n(x + 8)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44210\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 3\" width=\"280\" height=\"66\" \/><\/p>\n<p>Question 4.<br \/>\n(a &#8211; 6)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(a &#8211; 6)\u00b2 = a\u00b2 + 6\u00b2 &#8211; 2a(6)<br \/>\n= a\u00b2 + 36 &#8211; 12a<br \/>\n(a &#8211; 6)<sup>2 <\/sup>= a\u00b2 + 36 &#8211; 12a<\/p>\n<p>Question 5.<br \/>\n(2f &#8211; 1)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44211\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 5\" width=\"320\" height=\"69\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-5.png 320w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-5-300x65.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 6.<br \/>\n(5p + 2)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(5p + 2)\u00b2 = (5p)\u00b2 + (2)\u00b2 + 2(5p)(2)<br \/>\n= 25p\u00b2 + 4 + 20p<\/p>\n<p>Question 7.<br \/>\n(-7t + 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44212\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 7\" width=\"363\" height=\"68\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-7.png 363w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-7-300x56.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 8.<br \/>\n(-12 &#8211; n)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(-12 &#8211; n)\u00b2 = (-12)\u00b2 + n\u00b2 &#8211; 2(-12)n<br \/>\n= 144 + n\u00b2 + 24n<\/p>\n<p>Question 9.<br \/>\n(2a + b)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44213\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 9\" width=\"334\" height=\"67\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-9.png 334w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-9-300x60.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 10.<br \/>\n(6x &#8211; 3y)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(6x &#8211; 3y)\u00b2 = (6x)\u00b2 + (3y)\u00b2 &#8211; 2(6x)(3y)<br \/>\n= 36x\u00b2 + 9y\u00b2 &#8211; 36xy<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 11\u201314, write a polynomial that represents the area of the square.<br \/>\nQuestion 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36605\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 6\" width=\"118\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44214\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 11\" width=\"275\" height=\"66\" \/><\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36606\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 7\" width=\"141\" height=\"149\" \/><br \/>\nAnswer:<br \/>\n(2x + 7)\u00b2 = (2x)\u00b2 + 7\u00b2 + 2(2x)(7)<br \/>\n= 4x\u00b2 + 49 + 28x<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36607\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 8\" width=\"129\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44215\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 13\" width=\"337\" height=\"67\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-13.png 337w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-13-300x60.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p>Question 14.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36608\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 9\" width=\"119\" height=\"117\" \/><br \/>\nAnswer:<br \/>\n(4c + 4d)\u00b2 = (4c)\u00b2 + (4d)\u00b2 + 2(4c)(4d)<br \/>\n= 16c\u00b2 + 16d\u00b2 + 32cd<\/p>\n<p><strong>In Exercises 15\u201324, find the product.<\/strong><br \/>\nQuestion 15.<br \/>\n(t &#8211; 7)(t + 7)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44216\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 15\" width=\"244\" height=\"69\" \/><\/p>\n<p>Question 16.<br \/>\n(m + 6)(m &#8211; 6)<br \/>\nAnswer:<br \/>\n(m + 6)(m &#8211; 6) = m\u00b2 &#8211; 6\u00b2<br \/>\n= m\u00b2 &#8211; 36<\/p>\n<p>Question 17.<br \/>\n(4x + 1)(4x &#8211; 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44217\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 17\" width=\"294\" height=\"62\" \/><\/p>\n<p>Question 18.<br \/>\n(2k &#8211; 4)(2k + 4)<br \/>\nAnswer:<br \/>\n(2k &#8211; 4)(2k + 4) = (2k)\u00b2 &#8211; (4)\u00b2<br \/>\n= 4k\u00b2 &#8211; 16<\/p>\n<p>Question 19.<br \/>\n(8 + 3a)(8 &#8211; 3a)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44218\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 19\" width=\"296\" height=\"64\" \/><\/p>\n<p>Question 20.<br \/>\n(\\(\\frac{1}{2}\\) &#8211; c )(\\(\\frac{1}{2}\\) + c )<br \/>\nAnswer:<br \/>\n(\\(\\frac{1}{2}\\) &#8211; c )(\\(\\frac{1}{2}\\) + c ) = \\(\\frac{1}{2}\\)\u00b2 &#8211; c\u00b2<br \/>\n= \\(\\frac{1}{4}\\) &#8211; c\u00b2<\/p>\n<p>Question 21.<br \/>\n(p &#8211; 10q)(p + 10q)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44219\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 21\" width=\"339\" height=\"70\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-21.png 339w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-21-300x62.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 22.<br \/>\n(7m + 8n)(7m &#8211; 8n)<br \/>\nAnswer:<br \/>\n(7m + 8n)(7m &#8211; 8n) = (7m)\u00b2 &#8211; (8n)\u00b2<br \/>\n49m\u00b2 &#8211; 64n\u00b2<\/p>\n<p>Question 23.<br \/>\n(-y + 4)(-y &#8211; 4)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44220\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 23\" width=\"323\" height=\"66\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-23.png 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-23-300x61.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 24.<br \/>\n(-5g &#8211; 2h)(-5g + 2h)<br \/>\nAnswer:<br \/>\n(-5g &#8211; 2h)(-5g + 2h) = (-5g)\u00b2 &#8211; (2h)\u00b2<br \/>\n= 25g\u00b2 &#8211; 4h\u00b2<\/p>\n<p><strong>In Exercises 25\u201330, use special product patterns to find the product.<\/strong><br \/>\nQuestion 25.<br \/>\n16 \u2022 24<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44221\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 25\" width=\"273\" height=\"132\" \/><\/p>\n<p>Question 26.<br \/>\n33 \u2022 27<br \/>\nAnswer:<br \/>\n33 \u2022 27 = (30 + 3)(30 &#8211; 3)<br \/>\n(30 + 3)(30 &#8211; 3) = 30\u00b2 &#8211; 3\u00b2<br \/>\n= 900 &#8211; 9<br \/>\n= 891<\/p>\n<p>Question 27.<br \/>\n42<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44222\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 27\" width=\"263\" height=\"138\" \/><\/p>\n<p>Question 28.<br \/>\n29<sup>2<\/sup><br \/>\nAnswer:<br \/>\n29\u00b2 = (30 &#8211; 1)\u00b2<br \/>\n(30 &#8211; 1)\u00b2 = 30\u00b2 + 1\u00b2 &#8211; 2(30)(1)<br \/>\n= 900 + 1 &#8211; 60<br \/>\n= 841<\/p>\n<p>Question 29.<br \/>\n30.5<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44223\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 29\" width=\"310\" height=\"134\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-29.png 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-29-300x130.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 30.<br \/>\n10\\(\\frac{1}{3}\\) \u2022 9\\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n(10 &#8211; \\(\\frac{1}{3}\\))(10 + \\(\\frac{1}{3}\\)) = 10\u00b2 &#8211; \\(\\frac{1}{3}\\)\u00b2<br \/>\n= 100 &#8211; \\(\\frac{1}{9}\\)<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 31 and 32, describe and correct the error in finding the product.<br \/>\nQuestion 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36609\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 10\" width=\"220\" height=\"75\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44224\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 31\" width=\"558\" height=\"129\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-31.png 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-31-300x69.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36610\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 11\" width=\"325\" height=\"80\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-11.png 325w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-11-300x74.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nAnswer:<br \/>\n(s + 5)(s &#8211; 5) = s\u00b2 &#8211; 5\u00b2<br \/>\n= s\u00b2 &#8211; 25<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA contractor extends a house on two sides.<br \/>\na. The area of the house after the renovation is represented by (x + 50)<sup>2<\/sup>. Find this product.<br \/>\nb. Use the polynomial in part (a) to fond the area when x = 15. What is the area of the extension?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36611\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-12.1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 12.1\" width=\"222\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44225\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 33\" width=\"594\" height=\"387\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-33.png 594w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-33-300x195.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA square-shaped parking lot with 100-foot sides is reduced by x feet on one side and extended by x feet on an adjacent side.<br \/>\na. The area of the new parking lot is represented by (100 &#8211; x)(100 + x). Find this product.<br \/>\nAnswer:<br \/>\n(100 &#8211; x)(100 + x)<br \/>\n(100 &#8211; x)(100 + x) = 100\u00b2 &#8211; x\u00b2<br \/>\n= 10000 &#8211; x\u00b2<\/p>\n<p>b. Does the area of the parking lot increase, decrease, or stay the same? Explain.<br \/>\nAnswer:<br \/>\nThe original area is 100 \u00d7 100 = 10,000 sq. ft<br \/>\nThe new area is 10,000 &#8211; (10000 &#8211; x\u00b2) &#8211; x\u00b2<br \/>\nSo, the area of the parking lot decreases and decreased by x\u00b2<\/p>\n<p>c. Use the polynomial in part (a) to find the area of the new parking lot when x = 21.<br \/>\nAnswer:<br \/>\n10000 &#8211; x\u00b2<br \/>\nwhen x = 21<br \/>\n10000 &#8211; x\u00b2<br \/>\n= 10000 &#8211; 21\u00b2<br \/>\n= 10,000 &#8211; 441<br \/>\n= 9559 sq. ft<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn deer, the gene N is for normal coloring and the gene a is for no coloring, or albino. Any gene combination with an N results in normal coloring. The Punnett square shows the possible gene combinations of an offspring and the resulting colors from parents that both have the gene combination Na.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36612\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-12.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 12\" width=\"208\" height=\"202\" \/><br \/>\na. What percent of the possible gene combinations result in albino coloring?<br \/>\nb. Show how you could use a polynomial to model the possible gene combinations of the offspring.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44226\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 35\" width=\"598\" height=\"302\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-35.png 598w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-35-300x152.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour iris controls the amount of light that enters your eye by changing the size of your pupil.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36613\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 13\" width=\"160\" height=\"112\" \/><br \/>\na. Write a polynomial that represents the area of your pupil. Write your answer in terms of \u03c0.<br \/>\nAnswer:<br \/>\nr = 6 &#8211; x<br \/>\nA = \u03c0(6 &#8211; x)\u00b2<br \/>\nA = \u03c0(6\u00b2 + x\u00b2 &#8211; 2.6(x))<br \/>\nA = \u03c0(36 + x\u00b2 &#8211; 12x)<br \/>\nA = \u03c0(x\u00b2 &#8211; 12x + 36)<\/p>\n<p>b. The width x of your iris decreases from 4\ue03emillimeters to 2 millimeters when you enter a dark room. How many times greater is the area of your pupil after entering the room than before entering the room? Explain.<br \/>\nAnswer:<br \/>\nArea after entering\/Area before entering = \u03c0(2\u00b2 &#8211; 12(2) + 36)\/\u03c0(4\u00b2 &#8211; 12(4) + 36)<br \/>\n= 16\u03c0\/4\u03c0<br \/>\n= 4<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWrite two binomials that have the product x<sup>2<\/sup> &#8211; 121. Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44227\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 37\" width=\"570\" height=\"161\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-37.png 570w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-37-300x85.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nIn pea plants, any gene combination with a green gene (G) results in a green pod. The Punnett square shows the possible gene combinations of the offspring of two Gy pea plants and the resulting pod colors.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36614\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-14.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.3 14\" width=\"314\" height=\"184\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-14.png 314w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.3-14-300x176.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nA polynomial that models the possible gene combinations of the offspring is<br \/>\n(0.5G + 0.5y)<sup>2<\/sup> &#8211; 0.25G<sup>2<\/sup> + 0.5Gy + 0.25y<sup>2<\/sup>.<br \/>\nDescribe two ways to determine the percent of possible gene combinations that result in green pods.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 39\u201342, find the product.<\/strong><br \/>\nQuestion 39.<br \/>\n(x<sup>2<\/sup> + 1)(x<sup>2<\/sup> &#8211; 1)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44228\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 39\" width=\"291\" height=\"65\" \/><\/p>\n<p>Question 40.<br \/>\n(y<sup>3<\/sup> + 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(y<sup>3<\/sup> + 4)\u00b2 = (y\u00b3)\u00b2 + 4\u00b2 + 2y\u00b3(4)<br \/>\n= y<sup>6<\/sup> + 16 + 8y\u00b3<\/p>\n<p>Question 41.<br \/>\n(2m<sup>2<\/sup> &#8211; 5n<sup>2<\/sup>)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44229\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 41\" width=\"455\" height=\"103\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-41.png 455w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-41-300x68.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 42.<br \/>\n(r<sup>3<\/sup> &#8211; 6t<sup>4<\/sup>)(r<sup>3<\/sup> + 6t<sup>4<\/sup>)<br \/>\nAnswer:<br \/>\n(r<sup>3<\/sup> &#8211; 6t<sup>4<\/sup>)(r<sup>3<\/sup> + 6t<sup>4<\/sup>) = (r<sup>3<\/sup>)\u00b2 &#8211; (6t<sup>4<\/sup>)\u00b2<br \/>\n= r<sup>6<\/sup> &#8211; 36t<sup>8<\/sup><\/p>\n<p>Question 43.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims to be able to use a special product pattern to determine that (4\\(\\frac{1}{3}\\))<sup>2<\/sup> is equal to 16\\(\\frac{1}{9}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44230\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 43\" width=\"559\" height=\"151\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-43.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-43-300x81.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe area (in square meters) of the surface of an artificial lake is represented by x<sup>2<\/sup>. Describe three ways to modify the dimensions of the lake so that the new area can be represented by the three types of special product patterns discussed in this section.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind k so that 9x<sup>2<\/sup> &#8211; 48x + k is the square of a binomial.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44231\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 45\" width=\"533\" height=\"496\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-45.png 533w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-45-300x279.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nFind (x + 1)<sup>3<\/sup> and (x + 2)<sup>3<\/sup>. Find a pattern in the terms and use it to write a pattern for the cube of a binomial (a + b)<sup>3<\/sup>.<br \/>\nAnswer:<br \/>\n(x + 1)\u00b3 = (x)\u00b3 + (1)\u00b3 + 3(x)\u00b2(1) + 3(x)(1)\u00b2<br \/>\nx\u00b3 + 1 + 3x\u00b2 + 3x<br \/>\n(x + 1)\u00b3 = x\u00b3 + 1 + 3x\u00b2 + 3x<br \/>\n(x + 2)\u00b3 = (x)\u00b3 + (2)\u00b3 + 3(x)\u00b2(2) + 3(x)(2)\u00b2<br \/>\nx\u00b3 + 8 + 6x\u00b2 + 12x<br \/>\n(x + 2)\u00b3 = x\u00b3 + 8 + 6x\u00b2 + 12x<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFind two numbers a and b such that (a + b)(a &#8211; b) &lt; (a &#8211; b)<sup>2<\/sup> &lt; (a + b)<sup>2<\/sup>.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44232\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 47\" width=\"554\" height=\"220\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-47.png 554w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-47-300x119.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><br \/>\nQuestion 48.<br \/>\n12y &#8211; 18<br \/>\nAnswer: 12y &#8211; 18 = 6(2y &#8211; 3)<\/p>\n<p>Question 49.<br \/>\n9r + 27<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44233\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 49\" width=\"194\" height=\"35\" \/><\/p>\n<p>Question 50.<br \/>\n49s + 35t<br \/>\nAnswer: 49s + 35t = 7(7s + 5t)<\/p>\n<p>Question 51.<br \/>\n15x &#8211; 10y<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44234\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.3-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.3 Question 51\" width=\"235\" height=\"31\" \/><\/p>\n<h3><a id=\"Lesson_7.4_Solving_Polynomial_Equations_in_Factored_Form\"><\/a>Lesson 7.4 Solving Polynomial Equations in Factored Form<\/h3>\n<p><strong>Essential Question<\/strong> How can you solve a polynomial equation?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Matching Equivalent Forms of an Equation<br \/>\nWork with a partner. An equation is considered to be in factored form when the product of the factors is equal to 0. Match each factored form of the equation with its equivalent standard form and nonstandard form. Factored Form Standard Form Nonstandard Form<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36615\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 1\" width=\"502\" height=\"177\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-1.png 502w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-1-300x106.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Answer:<br \/>\na. (x &#8211; 1)(x &#8211; 3) = 0<br \/>\nx(x &#8211; 3) &#8211; 1(x &#8211; 3) = 0<br \/>\nx\u00b2 &#8211; 3x &#8211; 1x + 3 = 0<br \/>\nx\u00b2 &#8211; 4x + 3 = 0<br \/>\na = C = 5<\/p>\n<p>b. (x &#8211; 2)(x &#8211; 3) = 0<br \/>\nx(x &#8211; 3) &#8211; 2(x &#8211; 3) = 0<br \/>\nx\u00b2 &#8211; 3x &#8211; 2x + 6 = 0<br \/>\nx\u00b2 &#8211; 5x + 6 = 0<br \/>\nx\u00b2 &#8211; 5x = -6<br \/>\nb = D = 1<\/p>\n<p>c. (x + 1)(x &#8211; 2) = 0<br \/>\nx(x &#8211; 2) + 1(x &#8211; 2) = 0<br \/>\nx\u00b2 &#8211; 2x + 1x &#8211; 2 = 0<br \/>\nx\u00b2 &#8211; x &#8211; 2 = 0<br \/>\nc = A = 3<\/p>\n<p>d. (x &#8211; 1)(x + 2) = 0<br \/>\nx(x + 2) &#8211; 1(x + 2) = 0<br \/>\nx\u00b2 + 2x &#8211; 1x &#8211; 2 = 0<br \/>\nx\u00b2 + x &#8211; 2 = 0<br \/>\nd = B = 4<\/p>\n<p>e. (x + 1)(x &#8211; 3) = 0<br \/>\nx(x &#8211; 3) + 1(x &#8211; 3) = 0<br \/>\nx\u00b2 &#8211; 3x + x &#8211; 3 = 0<br \/>\nx\u00b2 &#8211; 2x &#8211; 3 = 0<br \/>\ne = E = 2<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing a Conjecture<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36616\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 2\" width=\"231\" height=\"179\" \/><br \/>\nWork with a partner. Substitute 1, 2, 3, 4, 5, and 6 for x in each equation and determine whether the equation is true. Organize your results in a table. Write a conjecture describing what you discovered.<br \/>\na. (x &#8211; 1)(x &#8211; 2) = 0<br \/>\nb. (x &#8211; 2)(x &#8211; 3) = 0<br \/>\nc. (x &#8211; 3)(x &#8211; 4) = 0<br \/>\nd. (x &#8211; 4)(x &#8211; 5) = 0<br \/>\ne. (x &#8211; 5)(x &#8211; 6) = 0<br \/>\nf. (x &#8211; 6)(x &#8211; 1) = 0<br \/>\nAnswer:<br \/>\na. (x &#8211; 1)(x &#8211; 2) = 0<br \/>\nx &#8211; 1 = 0 or x &#8211; 2 = 0<br \/>\nx = 1 or x = 2<br \/>\nx = 1, 2<br \/>\nb. (x &#8211; 2)(x &#8211; 3) = 0<br \/>\nx &#8211; 2 or x &#8211; 3 = 0<br \/>\nx = 2 or x = 3<br \/>\nx = 2, 3<br \/>\nc. (x &#8211; 3)(x &#8211; 4) = 0<br \/>\nx &#8211; 3 = 0 or x &#8211; 4 = 0<br \/>\nx = 3 or x = 4<br \/>\nx = 3, 4<br \/>\nd. (x &#8211; 4)(x &#8211; 5) = 0<br \/>\nx &#8211; 4 = 0 or x &#8211; 5 = 0<br \/>\nx = 4 or x = 5<br \/>\nx = 4, 5<br \/>\ne. (x &#8211; 5)(x &#8211; 6) = 0<br \/>\nx &#8211; 5 = 0 or x &#8211; 6 = 0<br \/>\nx = 5 or x = 6<br \/>\nx = 5, 6<br \/>\nf. (x &#8211; 6)(x &#8211; 1) = 0<br \/>\nx &#8211; 6 = 0 or x &#8211; 1 = 0<br \/>\nx = 6 or x = 1<br \/>\nx = 1, 6<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Special Properties of 0 and 1<br \/>\nWork with a partner. The numbers 0 and 1 have special properties that are shared by no other numbers. For each of the following, decide whether the property is true for 0, 1, both, or neither. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36617\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 3\" width=\"480\" height=\"181\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-3.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-3-300x113.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\nAnswer:<br \/>\na. When you add <strong>0<\/strong> to a number n, you get n.<br \/>\nb. If the product of two numbers is <strong>0<\/strong>, then at least one of the numbers is 0.<br \/>\nc. The square of <strong>1<\/strong> is equal to itself.<br \/>\nd. When you multiply a number n by <strong>1<\/strong>, you get n.<br \/>\ne. When you multiply a number n by <strong>0<\/strong>, you get 0.<br \/>\nf. The opposite of <strong>0<\/strong> is equal to itself.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you solve a polynomial equation?<br \/>\nAnswer:<br \/>\n1. Write the equation in a correct form<br \/>\n2. Use factoring strategies to factor in the problem.<br \/>\n3. Use the zero product property and set each factor containing a variable equal to zero.<br \/>\n4. Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.<\/p>\n<p>Question 5.<br \/>\nOne of the properties in Exploration 3 is called the Zero-Product Property. It is one of the most important properties in all of algebra. Which property is it? Why do you think it is called the Zero-Product Property? Explain how it is used in algebra and why it is so important.<br \/>\nAnswer:<br \/>\nThe most important property in all algebra is the Zero product property.<br \/>\nThe product of given numbers must be zero, so it is called zero product property.<br \/>\nIn algebra, for solving the equation having the expression equals zero, first we have to factor and use the zero product property to find the solutions.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation. Check your solutions.<\/strong><br \/>\nQuestion 1.<br \/>\nx(x &#8211; 1) = 0<br \/>\nAnswer: x = 0, 1<\/p>\n<p>Explanation:<br \/>\nx(x &#8211; 1) = 0<br \/>\nx = 0 or x &#8211; 1 = 0<br \/>\nx = 0 or x = 1<br \/>\nx = 0, 1<\/p>\n<p>Question 2.<br \/>\n3t(t + 2) = 0<br \/>\nAnswer: t = 0, -2<\/p>\n<p>Explanation:<br \/>\n3t(t + 2) = 0<br \/>\n3t = 0 or t + 2 = 0<br \/>\nt = 0 or t = -2<br \/>\nt = 0, -2<\/p>\n<p>Question 3.<br \/>\n(z &#8211; 4)(z &#8211; 6) = 0<br \/>\nAnswer: z = 4, 6<\/p>\n<p>Explanation:<br \/>\n(z &#8211; 4)(z &#8211; 6) = 0<br \/>\nz &#8211; 4 = 0 or z &#8211; 6 = 0<br \/>\nz = 4 or z = 6<br \/>\nz = 4, 6<\/p>\n<p><strong>Solve the equation. Check your solutions.<\/strong><br \/>\nQuestion 4.<br \/>\n(3s + 5)(5s + 8) = 0<br \/>\nAnswer: s = -5\/3, -8\/5<\/p>\n<p>Explanation:<br \/>\n(3s + 5)(5s + 8) = 0<br \/>\n3s + 5 = 0 or 5s + 8 = 0<br \/>\n3s = -5 or 5s = -8<br \/>\ns = -5\/3 or s = -8\/5<br \/>\ns = -5\/3, -8\/5<\/p>\n<p>Question 5.<br \/>\n(b + 7)<sup>2<\/sup> = 0<br \/>\nAnswer: b = -7<\/p>\n<p>Explanation:<br \/>\n(b + 7)<sup>2<\/sup> = 0<br \/>\nb + 7 = 0<br \/>\nb = -7<\/p>\n<p>Question 6.<br \/>\n(d &#8211; 2)(d + 6)(d + 8) = 0<br \/>\nAnswer: d = 2, -6, -8<\/p>\n<p>Explanation:<br \/>\n(d &#8211; 2)(d + 6)(d + 8) = 0<br \/>\nd &#8211; 2 = 0 or d + 6 = 0 or d + 8 = 0<br \/>\nd = 2 or d = -6 or d = -8<br \/>\nd = 2, -6, -8<\/p>\n<p>Question 7.<br \/>\nFactor out the greatest common monomial factor from 8y<sup>2<\/sup> &#8211; 24y.<br \/>\nAnswer:<br \/>\n8y<sup>2<\/sup> &#8211; 24y<br \/>\nTake 8y as common<br \/>\n8y(y &#8211; 3)<br \/>\n8y = 0 or y &#8211; 3 = 0<br \/>\ny = 0 or y = 3<br \/>\ny = 0, 3<\/p>\n<p><strong>Solve the equation. Check your solutions.<\/strong><br \/>\nQuestion 8.<br \/>\na<sup>2<\/sup> + 5a = 0<br \/>\nAnswer: a = 0, -5<\/p>\n<p>Explanation:<br \/>\na<sup>2<\/sup> + 5a = 0<br \/>\na(a + 5) = 0<br \/>\na = 0 or a + 5 = 0<br \/>\na = 0 or a = -5<br \/>\na = 0, -5<\/p>\n<p>Question 9.<br \/>\n3s<sup>2<\/sup> &#8211; 9s = 0<br \/>\nAnswer: s = 0, 3<\/p>\n<p>Explanation:<br \/>\n3s<sup>2<\/sup> &#8211; 9s = 0<br \/>\n3s(s &#8211; 3) = 0<br \/>\n3s = 0 or s &#8211; 3 = 0<br \/>\ns = 0 or s = 3<br \/>\ns = 0, 3<\/p>\n<p>Question 10.<br \/>\n4x<sup>2<\/sup> = 2x<br \/>\nAnswer: x = 1\/2<\/p>\n<p>Explanation:<br \/>\n4x<sup>2<\/sup> = 2x<br \/>\n2x(2x) = 2x<br \/>\n2x = 1<br \/>\nx = 1\/2<\/p>\n<p>Question 11.<br \/>\nYou can model the entrance to a mine shaft using the equation y = &#8211; \\(\\frac{1}{2}\\)(x + 4)(x &#8211; 4), where x and y are measured in feet. The x-axis represents the ground. Find the width of the entrance at ground level.<br \/>\nAnswer:<br \/>\nGiven equation is,<br \/>\ny = &#8211; \\(\\frac{1}{2}\\)(x + 4)(x &#8211; 4)<br \/>\n1\/2 \u00d7 2 = -1<br \/>\ny = -1(x + 4)(x &#8211; 4)<br \/>\nx + 4 = 0 or x &#8211; 4 = 0<br \/>\nx = -4 or x = 4<br \/>\n4 &#8211; (-4) = 4 + 4 = 8 feet<br \/>\nwidth = 8 feet<\/p>\n<h3><a id=\"Solving_Polynomial_Equations_in_Factored_Form_7.4_Exercises\"><\/a>Solving Polynomial Equations in Factored Form 7.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to use the Zero-Product Property to find the solutions of the equation 3x(x &#8211; 6) = 0.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44235\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 1\" width=\"576\" height=\"108\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-1.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-1-300x56.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find both answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36618\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 4\" width=\"453\" height=\"118\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-4.png 453w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-4-300x78.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><br \/>\nAnswer:<br \/>\n(2k + 4) + (k &#8211; 3) = 0<br \/>\n2k + 4 + k &#8211; 3 = 0<br \/>\n(2k + 4) + (k &#8211; 3) = 0 is different with others.<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, solve the equation.<\/strong><br \/>\nQuestion 3.<br \/>\nx(x + 7) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44236\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 3\" width=\"313\" height=\"166\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-3.png 313w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-3-300x159.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<p>Question 4.<br \/>\nr(r &#8211; 10) = 0<br \/>\nAnswer: r = 0, 10<\/p>\n<p>Explanation:<br \/>\nr(r &#8211; 10) = 0<br \/>\nr = 0 or r &#8211; 10 = 0<br \/>\nr = 0 or r = 10<br \/>\nr = 0, 10<\/p>\n<p>Question 5.<br \/>\n12t(t &#8211; 5) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44237\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 5\" width=\"305\" height=\"183\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-5.png 305w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-5-300x180.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 6.<br \/>\n-2v(v + 1) = 0<br \/>\nAnswer: v = 0, -1<\/p>\n<p>Explanation:<br \/>\n-2v(v + 1) = 0<br \/>\n-2v = 0 or v + 1 = 0<br \/>\nv = 0 or v = -1<br \/>\nv = 0, -1<\/p>\n<p>Question 7.<br \/>\n(s &#8211; 9)(s &#8211; 1) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44238\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 7\" width=\"338\" height=\"168\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-7.png 338w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-7-300x149.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 8.<br \/>\n(y + 2)(y &#8211; 6) = 0<br \/>\nAnswer: y = -2, 6<\/p>\n<p>Explanation:<br \/>\n(y + 2)(y &#8211; 6) = 0<br \/>\ny + 2 = 0 or y &#8211; 6 = 0<br \/>\ny = -2 or y = 6<br \/>\ny = -2, 6<\/p>\n<p><strong>In Exercises 9\u201320, solve the equation.<\/strong><br \/>\nQuestion 9.<br \/>\n(2a &#8211; 6)(3a + 15) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44239\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 9\" width=\"411\" height=\"259\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-9.png 411w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-9-300x189.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 10.<br \/>\n(4q + 3)(q + 2) = 0<br \/>\nAnswer: q = -3\/4, -2<\/p>\n<p>Explanation:<br \/>\n(4q + 3)(q + 2) = 0<br \/>\n4q + 3 = 0 or q + 2 = 0<br \/>\n4q = -3 or q = -2<br \/>\nq = -3\/4 or q = -2<br \/>\nq = -3\/4, -2<\/p>\n<p>Question 11.<br \/>\n(5m + 4)<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44240\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 11\" width=\"442\" height=\"349\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-11.png 442w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-11-300x237.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 12.<br \/>\n(h &#8211; 8)<sup>2<\/sup> = 0<br \/>\nAnswer: h = 8<\/p>\n<p>Explanation:<br \/>\n(h &#8211; 8)<sup>2<\/sup> = 0<br \/>\nh &#8211; 8 = 0<br \/>\nh = 8<\/p>\n<p>Question 13.<br \/>\n(3 &#8211; 2g)(7 &#8211; g) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44241\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 13\" width=\"402\" height=\"320\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-13.png 402w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-13-300x239.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 14.<br \/>\n(2 &#8211; 4d )(2 + 4d ) = 0<br \/>\nAnswer: d = 1\/2 or d = -1\/2<\/p>\n<p>Explanation:<br \/>\n(2 &#8211; 4d )(2 + 4d ) = 0<br \/>\n2 &#8211; 4d = 0 or 2 + 4d = 0<br \/>\n2 = 4d or 2 = -4d<br \/>\n1 = 2d or 1 = -2d<br \/>\nd = 1\/2 or d = -1\/2<\/p>\n<p>Question 15.<br \/>\nz(z + 2)(z &#8211; 1) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44242\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 15\" width=\"495\" height=\"165\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-15.png 495w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-15-300x100.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 16.<br \/>\n5p(2p &#8211; 3)(p + 7) = 0<br \/>\nAnswer: p = 0, 3\/2, -7<\/p>\n<p>Explanation:<br \/>\n5p(2p &#8211; 3)(p + 7) = 0<br \/>\n5p = 0 or 2p &#8211; 3 = 0 or p + 7 = 0<br \/>\np = 0 or p = 3\/2 or p = -7<br \/>\np = 0, 3\/2, -7<\/p>\n<p>Question 17.<br \/>\n(r &#8211; 4)<sup>2<\/sup>(r + 8) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44243\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 17\" width=\"536\" height=\"253\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-17.png 536w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-17-300x142.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 18.<br \/>\nw(w &#8211; 6)<sup>2<\/sup> = 0<br \/>\nAnswer: w = 0, 6<\/p>\n<p>Explanation:<br \/>\nw(w &#8211; 6)<sup>2<\/sup> = 0<br \/>\nw = 0 or (w &#8211; 6)\u00b2 = 0<br \/>\nw = 0 or w &#8211; 6 = 0<br \/>\nw = 0 or w = 6<br \/>\nw = 0, 6<\/p>\n<p>Question 19.<br \/>\n(15 &#8211; 5c)(5c + 5)(-c + 6) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44244\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 19\" width=\"603\" height=\"270\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-19.png 603w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-19-300x134.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 20.<br \/>\n(2 &#8211; n) ( 6 + \\(\\frac{2}{3}\\)n ) (n &#8211; 2) = 0<br \/>\nAnswer: n = 2, -9<\/p>\n<p>Explanation:<br \/>\n(2 &#8211; n) ( 6 + \\(\\frac{2}{3}\\)n ) (n &#8211; 2) = 0<br \/>\n2 &#8211; n = 0 or 6 + \\(\\frac{2}{3}\\)n = 0 or n &#8211; 2 = 0<br \/>\nn = 2 or \\(\\frac{2}{3}\\)n = -6 or n = 2<br \/>\nn = 2 or n = -18\/2 or n = 2<br \/>\nn = 2 or n = -9 or n = 2<br \/>\nn = 2, -9<\/p>\n<p><strong>In Exercises 21\u201324, find the x-coordinates of the points where the graph crosses the x-axis.<\/strong><br \/>\nQuestion 21.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36619\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 5\" width=\"154\" height=\"216\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44245\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 21\" width=\"551\" height=\"247\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-21.png 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-21-300x134.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 22.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36620\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 6\" width=\"147\" height=\"218\" \/><br \/>\nAnswer:<br \/>\ny = (x + 1)(x + 7)<br \/>\n(x + 1)(x + 7) = 0<br \/>\nx + 1 = 0 or x + 7 = 0<br \/>\nx = -1 or x = -7<br \/>\nx = -1, -7<br \/>\nThe x-coordinates of the points where the graph crosses the x-axis are the roots x = -1 and -7.<\/p>\n<p>Question 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36621\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 7\" width=\"150\" height=\"209\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44246\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 23\" width=\"558\" height=\"302\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-23.png 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-23-300x162.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36622\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 8\" width=\"170\" height=\"212\" \/><br \/>\nAnswer:<br \/>\ny = -0.2(x + 22)(x &#8211; 15)<br \/>\n-0.2(x + 22)(x &#8211; 15) = 0<br \/>\n(x + 22)(x &#8211; 15) = 0<br \/>\nx + 22 = 0 or x &#8211; 15 = 0<br \/>\nx = -22 or x = 15<br \/>\nThe x-coordinates of the points where the graph crosses the x-axis are the roots x = -22 and 15.<\/p>\n<p><strong>In Exercises 25\u201330, factor the polynomial.<\/strong><br \/>\nQuestion 25.<br \/>\n5z<sup>2<\/sup> + 45z<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44247\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 25\" width=\"214\" height=\"34\" \/><\/p>\n<p>Question 26.<br \/>\n6d<sup>2<\/sup> &#8211; 21d<br \/>\nAnswer:<br \/>\n6d<sup>2<\/sup> &#8211; 21d<br \/>\nTake 3d as a common factor.<br \/>\n6d<sup>2<\/sup> &#8211; 21d = 3d(2d &#8211; 7)<\/p>\n<p>Question 27.<br \/>\n3y<sup>3<\/sup> &#8211; 9y<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44248\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 27\" width=\"229\" height=\"43\" \/><\/p>\n<p>Question 28.<br \/>\n20x<sup>3<\/sup> + 30x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n20x<sup>3<\/sup> + 30x<sup>2<\/sup><br \/>\nTake 10x\u00b2 as common.<br \/>\n20x<sup>3<\/sup> + 30x\u00b2 = 10x\u00b2(2x + 3)<\/p>\n<p>Question 29.<br \/>\n5n<sup>6<\/sup> + 2n<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44249\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 29\" width=\"231\" height=\"30\" \/><\/p>\n<p>Question 30.<br \/>\n12a<sup>4<\/sup> + 8a<br \/>\nAnswer:<br \/>\n12a<sup>4<\/sup> + 8a<br \/>\nTake 4a as common.<br \/>\n12a<sup>4<\/sup> + 8a = 4a(3a\u00b3 + 2)<\/p>\n<p><strong>In Exercises 31\u201336, solve the equation.<\/strong><br \/>\nQuestion 31.<br \/>\n4p<sup>2<\/sup> &#8211; p = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44250\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 31\" width=\"312\" height=\"330\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-31.png 312w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-31-284x300.png 284w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Question 32.<br \/>\n6m<sup>2<\/sup> + 12m = 0<br \/>\nAnswer: m = 0, -2<\/p>\n<p>Explanation:<br \/>\n6m<sup>2<\/sup> + 12m = 0<br \/>\nTake 6m as common.<br \/>\n6m(m + 2) = 0<br \/>\n6m = 0 or m + 2 = 0<br \/>\nm = 0 or m = -2<br \/>\nm = 0, -2<\/p>\n<p>Question 33.<br \/>\n25c + 10c<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44251\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 33\" width=\"379\" height=\"341\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-33.png 379w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-33-300x270.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 34.<br \/>\n18q &#8211; 2q<sup>2<\/sup> = 0<br \/>\nAnswer: q = 0, 9<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n2q(9 &#8211; q) = 0<br \/>\n2q = 0 or 9 &#8211; q = 0<br \/>\nq = 0 or 9 = q<br \/>\nq = 0, 9<\/p>\n<p>Question 35.<br \/>\n3n<sup>2<\/sup> = 9n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44252\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 35\" width=\"364\" height=\"293\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-35.png 364w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-35-300x241.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>Question 36.<br \/>\n-28r = 4r<sup>2<br \/>\n<\/sup>Answer: q = 0, 9<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n-28r = 4r<sup>2<\/sup><br \/>\n4r\u00b2 + 28r = 0<br \/>\nTake 4r as common.<br \/>\n4r(r + 7) = 0<br \/>\n4r = 0 or r + 7 = 0<br \/>\nr = 0 or r = -7<\/p>\n<p>Question 37.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36623\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 9\" width=\"239\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44253\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 37\" width=\"583\" height=\"280\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-37.png 583w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-37-300x144.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36624\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 10\" width=\"239\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n3y\u00b2 = 21y<br \/>\n3y(y) = 3y(7)<br \/>\ny = 7<br \/>\nSo, y = 7 is the solution.<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe entrance of a tunnel can be modeled by y = &#8211; \\(\\frac{11}{50}\\)(x &#8211; 4)(x &#8211; 24), where x and y are measured in feet. The x-axis represents the ground. Find the width of the tunnel at ground level.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36625\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 11\" width=\"206\" height=\"181\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44254\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 39\" width=\"567\" height=\"373\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-39.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-39-300x197.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe Gateway Arch in St. Louis can be modeled by y = &#8211; \\(\\frac{2}{315}\\)(x + 315)(x &#8211; 315), where x and y are measured in feet. The x-axis represents the ground.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36626\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 12\" width=\"205\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-12.png 205w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-12-150x150.png 150w\" sizes=\"(max-width: 205px) 100vw, 205px\" \/><br \/>\na. Find the width of the arch at ground level.<br \/>\nb. How tall is the arch?<br \/>\nAnswer:<br \/>\ny = &#8211; \\(\\frac{2}{315}\\)(x + 315)(x &#8211; 315)<br \/>\nx-intercept are -315 and 315.<br \/>\nWidth = 315 &#8211; (-315) = 315 + 315 = 630 feet<br \/>\ny = -2\/315(x + 315)(x &#8211; 315)<br \/>\n= -2\/315(x\u00b2 &#8211; 315\u00b2)<br \/>\n= -2\/315x\u00b2 + 630<br \/>\nwhen x = 0, y = 630<br \/>\nHeight is 630 ft<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA penguin leaps out of the water while swimming. This action is called porpoising. The height y (in feet) of a porpoising penguin can be modeled by y = -16x<sup>2<\/sup> + 4.8x, where x is the time (in seconds) since the penguin leaped out of the water. Find the roots of the equation when y = 0. Explain what the roots mean in this situation.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44255\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 41\" width=\"576\" height=\"475\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-41.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-41-300x247.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to fill in each blank in the equation with the symbol + or -. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36627\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 13\" width=\"188\" height=\"215\" \/><br \/>\nAnswer:<br \/>\nWhen y = 0, (x &#8211; 5) or (x + 3)<br \/>\nx &#8211; 5 = 0 or x + 3 = 0<br \/>\nx = 5\u00a0 or x = -3<br \/>\ny = (x &#8211; 5)(x + 3)<\/p>\n<p>Question 43.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHow many x-intercepts does the graph of y = (2x + 5)(x &#8211; 9)<sup>2<\/sup> have? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44256\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 43\" width=\"539\" height=\"86\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-43.png 539w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-43-300x48.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that the graph of the equation y = (x &#8211; a)(x &#8211; b) always has two x-intercepts for any values of a and b. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\ny = (x &#8211; a)(x &#8211; b)<br \/>\n(x &#8211; a)(x &#8211; b) = 0<br \/>\nx &#8211; a = 0 or x &#8211; b = 0<br \/>\nx = a or x = b<br \/>\nx = a, b<br \/>\nSo, your friend is correct<\/p>\n<p>Question 45.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDoes the equation (x<sup>2<\/sup> + 3)(x<sup>4<\/sup>+ 1) = 0 have any real roots? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44257\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 45\" width=\"583\" height=\"233\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-45.png 583w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-45-300x120.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite a polynomial equation of degree 4 whose only roots are x = 1, x = 2, and x = 3.<br \/>\nAnswer:<br \/>\nx = 1 = x &#8211; 1 = 0<br \/>\nx = 2 = x &#8211; 2 = 0<br \/>\nx = 3 = x &#8211; 3 = 0<br \/>\nx = 1 = x &#8211; 1 = 0<br \/>\n(x &#8211; 1)(x &#8211; 1)(x &#8211; 2)(x &#8211; 3) = 0<\/p>\n<p>Question 47.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind the values of x in terms of y that are solutions of each equation.<br \/>\na. (x + y)(2x &#8211; y) = 0<br \/>\nb. (x<sup>2<\/sup> &#8211; y<sup>2<\/sup>)(4x + 16y) = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44258\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 47\" width=\"614\" height=\"565\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-47.png 614w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-47-300x276.png 300w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nSolve the equation (4<sup>x-5<\/sup> &#8211; 16)(3<sup>x<\/sup> &#8211; 81) = 0.<br \/>\nAnswer:<br \/>\n(4<sup>x-5<\/sup> &#8211; 16)(3<sup>x<\/sup> &#8211; 81) = 0<br \/>\n(4<sup>x-5<\/sup> &#8211; 16) = 0 or (3<sup>x<\/sup> &#8211; 81) = 0<br \/>\n4<sup>x-5<\/sup> &#8211; 16 = 0 or 3<sup>x<\/sup> &#8211; 81 = 0<br \/>\n4<sup>x-5<\/sup> &#8211; 4\u00b2 = 0 or 3<sup>x<\/sup> &#8211; 9\u00b2 = 0<br \/>\n4<sup>x-5<\/sup> = 4\u00b2 or 3<sup>x<\/sup> = 9\u00b2<br \/>\nx &#8211; 5 = 2 or x = 2<br \/>\nx = 2 + 5 or x = 2<br \/>\nx = 7, 2<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>List the factor pairs of the number.<\/strong><br \/>\nQuestion 49.<br \/>\n10<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44259\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 49\" width=\"483\" height=\"133\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-49.png 483w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-49-300x83.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><\/p>\n<p>Question 50.<br \/>\n18<br \/>\nAnswer:<br \/>\nThe factor pairs of 18 are<br \/>\n1 \u00d7 18<br \/>\n2 \u00d7 9<br \/>\n3 \u00d7 6<br \/>\nFactor pairs of 18 are 1, 2, 3, 6, 9, 18.<\/p>\n<p>Question 51.<br \/>\n30<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44260\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.4 Question 51\" width=\"583\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-51.png 583w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.4-Question-51-300x118.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 52.<br \/>\n48<br \/>\nAnswer:<br \/>\n48 = 1 \u00d7 48<br \/>\n2 \u00d7 24<br \/>\n3 \u00d7 16<br \/>\n4 \u00d7 12<br \/>\n6 \u00d7 8<br \/>\nFactor pairs of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.<\/p>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Study_Skills:_Preparing_for_a_Test\"><\/a>Polynomial Equations and Factoring Study Skills: Preparing for a Test<\/h3>\n<p><strong>7.1\u20137.4 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36628\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-14.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 14\" width=\"641\" height=\"95\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-14.png 641w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-14-300x44.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36629\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 15\" width=\"639\" height=\"257\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-15.png 639w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-15-300x121.png 300w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nExplain how you wrote the polynomial in Exercise 11 on page 375. Is there another method you can use to write the same polynomial?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nFind a shortcut for exercises like Exercise 7 on page 381 when the variable has a coefficient of 1. Does your shortcut work when the coefficient is not 1?<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Preparing for a Test<\/strong><\/p>\n<ul>\n<li>Review examples of each type of problem that could appear on the test.<\/li>\n<li>Review the homework problems your teacher assigned.<\/li>\n<li>Take a practice test<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36630\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-16.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.4 16\" width=\"358\" height=\"266\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-16.png 358w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.4-16-300x223.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/li>\n<\/ul>\n<h3><a id=\"Polynomial_Equations_and_Factoring_7.1\u20137.4_Quiz\"><\/a>Polynomial Equations and Factoring 7.1\u20137.4 Quiz<\/h3>\n<p>Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.<br \/>\nQuestion 1.<br \/>\n-8q<sup>3<\/sup><br \/>\nAnswer:<br \/>\n-8q\u00b3<br \/>\nThe coefficient of the polynomial is -8<br \/>\nThe degree of the polynomial is 3<br \/>\nNumber of terms = 1<br \/>\nThe name of the polynomial is monomial.<\/p>\n<p>Question 2.<br \/>\n9 + d<sup>2<\/sup> &#8211; 3d<br \/>\nAnswer:<br \/>\n9 + d<sup>2<\/sup> &#8211; 3d<br \/>\nThe coefficient of the polynomial is 1, -3<br \/>\nThe degree of the polynomial is 2<br \/>\nNumber of terms = 3<br \/>\nThe name of the polynomial is trinomial.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{2}{3}\\)m<sup>4<\/sup> &#8211; \\(\\frac{5}{6}\\)m<sup>6<\/sup><br \/>\nAnswer:<br \/>\n\\(\\frac{2}{3}\\)m<sup>4<\/sup> &#8211; \\(\\frac{5}{6}\\)m<sup>6<\/sup><br \/>\nThe coefficient of the polynomial is \\(\\frac{2}{3}\\), &#8211;\\(\\frac{5}{6}\\)<br \/>\nThe degree of the polynomial is 6<br \/>\nNumber of terms = 2<br \/>\nThe name of the polynomial is binomial.<\/p>\n<p>Question 4.<br \/>\n-1.3z + 3z<sup>4<\/sup> + 7.4z<sup>2<\/sup><br \/>\nAnswer:<br \/>\n-1.3z + 3z<sup>4<\/sup> + 7.4z<sup>2<\/sup><br \/>\nThe coefficient of the polynomial is 3, 7.4, -1.3<br \/>\nThe degree of the polynomial is 4<br \/>\nNumber of terms = 3<br \/>\nThe name of the polynomial is trinomial.<\/p>\n<p>Find the sum or difference.<br \/>\nQuestion 5.<br \/>\n(2x<sup>2<\/sup> + 5) + (-x<sup>2<\/sup> + 4)<br \/>\nAnswer:<br \/>\n(2x<sup>2<\/sup> + 5) + (-x<sup>2<\/sup> + 4)<br \/>\n2x<sup>2<\/sup> + 5 &#8211; x<sup>2<\/sup> + 4<br \/>\nx\u00b2 + 5 + 4<br \/>\nx\u00b2 + 9<br \/>\n(2x<sup>2<\/sup> + 5) + (-x<sup>2<\/sup> + 4) = x\u00b2 + 9<\/p>\n<p>Question 6.<br \/>\n(-3n<sup>2<\/sup> + n) &#8211; (2n<sup>2<\/sup> &#8211; 7)<br \/>\nAnswer:<br \/>\n(-3n<sup>2<\/sup> + n) &#8211; (2n<sup>2<\/sup> &#8211; 7)<br \/>\n-3n<sup>2<\/sup> + n &#8211; 2n<sup>2<\/sup> + 7<br \/>\n-3n\u00b2 + n &#8211; 7<br \/>\n(-3n<sup>2<\/sup> + n) &#8211; (2n<sup>2<\/sup> &#8211; 7) = -3n\u00b2 + n &#8211; 7<\/p>\n<p>Question 7.<br \/>\n(-p<sup>2<\/sup> + 4p) &#8211; (p<sup>2<\/sup> &#8211; 3p + 15)<br \/>\nAnswer:<br \/>\n(-p<sup>2<\/sup> + 4p) &#8211; (p<sup>2<\/sup> &#8211; 3p + 15)<br \/>\n-p<sup>2<\/sup> + 4p &#8211; p<sup>2<\/sup> + 3p &#8211; 15<br \/>\n-2p\u00b2 + 7p &#8211; 15<\/p>\n<p>Question 8.<br \/>\n(a<sup>2<\/sup> &#8211; 3ab + b<sup>2<\/sup>) + (-a<sup>2<\/sup> + ab + b<sup>2<\/sup>)<br \/>\nAnswer:<br \/>\n(a<sup>2<\/sup> &#8211; 3ab + b<sup>2<\/sup>) + (-a<sup>2<\/sup> + ab + b<sup>2<\/sup>)<br \/>\na\u00b2 &#8211; 3ab + b\u00b2 &#8211; a\u00b2 + ab + b\u00b2<br \/>\n-2ab + 2b\u00b2<br \/>\n(a<sup>2<\/sup> &#8211; 3ab + b<sup>2<\/sup>) + (-a<sup>2<\/sup> + ab + b<sup>2<\/sup>) = -2ab + 2b\u00b2<\/p>\n<p>Find the product.<br \/>\nQuestion 9.<br \/>\n(w + 6)(w + 7)<br \/>\nAnswer:<br \/>\n(w + 6)(w + 7)<br \/>\nw(w + 7) + 6(w + 7)<br \/>\nw\u00b2 + 7w + 6w + 42<br \/>\nw\u00b2 + 13w + 42<\/p>\n<p>Question 10.<br \/>\n(3 &#8211; 4d )(2d &#8211; 5)<br \/>\nAnswer:<br \/>\n(3 &#8211; 4d )(2d &#8211; 5)<br \/>\n3(2d &#8211; 5) &#8211; 4d(2d &#8211; 5)<br \/>\n6d &#8211; 15 &#8211; 8d\u00b2 + 20d<br \/>\n-8d\u00b2 + 26d &#8211; 15<\/p>\n<p>Question 11.<br \/>\n(y + 9)(y<sup>2<\/sup> + 2y &#8211; 3)<br \/>\nAnswer:<br \/>\n(y + 9)(y<sup>2<\/sup> + 2y &#8211; 3)<br \/>\ny(y<sup>2<\/sup> + 2y &#8211; 3) + 9(y<sup>2<\/sup> + 2y &#8211; 3)<br \/>\ny\u00b3 + 2y\u00b2 &#8211; 3y + 9y\u00b2 + 18y &#8211; 27<br \/>\ny\u00b3 + 11y\u00b2 + 15y &#8211; 27<\/p>\n<p>Question 12.<br \/>\n(3z &#8211; 5)(3z + 5)<br \/>\nAnswer:<br \/>\n(3z &#8211; 5)(3z + 5) = (3z)\u00b2 &#8211; (5)\u00b2<br \/>\n= 9z\u00b2 &#8211; 25<\/p>\n<p>Question 13.<br \/>\n(t + 5)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(t + 5)<sup>2 <\/sup>=t\u00b2 + 5\u00b2 + 2(t)(5)<br \/>\n= t\u00b2 + 25 + 10t<\/p>\n<p>Question 14.<br \/>\n(2q &#8211; 6)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(2q &#8211; 6)\u00b2 = (2q)\u00b2 + 6\u00b2 &#8211; 2(2q)(6)<br \/>\n= 4q\u00b2 + 36 &#8211; 24q<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 15.<br \/>\n5x<sup>2<\/sup> &#8211; 15x = 0<br \/>\nAnswer: x = 0, 3<\/p>\n<p>Explanation:<br \/>\n5x<sup>2<\/sup> &#8211; 15x = 0<br \/>\n5x(x &#8211; 3) = 0<br \/>\n5x = 0 or x &#8211; 3 = 0<br \/>\nx = 0 or x = 3<br \/>\nx = 0, 3<\/p>\n<p>Question 16.<br \/>\n(8 &#8211; g)(8 &#8211; g) = 0<br \/>\nAnswer: g = 8<\/p>\n<p>Explanation:<br \/>\n(8 &#8211; g)(8 &#8211; g) = 0<br \/>\n8 &#8211; g = 0 or 8 &#8211; g = 0<br \/>\ng = 8<\/p>\n<p>Question 17.<br \/>\n(3p + 7)(3p &#8211; 7)( p + 8) = 0<br \/>\nAnswer: p = -7\/3, 7\/3, -8<\/p>\n<p>Explanation:<br \/>\n(3p + 7)(3p &#8211; 7)( p + 8) = 0<br \/>\n3p + 7 = 0 or 3p &#8211; 7 = 0 or p + 8 = 0<br \/>\n3p = -7 or 3p = 7 or p = -8<br \/>\np = -7\/3, 7\/3, -8<\/p>\n<p>Question 18.<br \/>\n-3y( y &#8211; 8)(2y + 1) = 0<br \/>\nAnswer: y = 0, 8, -1\/2<\/p>\n<p>Explanation:<br \/>\n-3y( y &#8211; 8)(2y + 1) = 0<br \/>\n-3y = 0 or y &#8211; 8 = 0 or 2y + 1 = 0<br \/>\ny = 0 or y = 8 or y = -1\/2<br \/>\ny = 0, 8, -1\/2<\/p>\n<p>Question 19.<br \/>\nYou are making a blanket with a fringe border of equal width on each side.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36631\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-q-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring q 1\" width=\"256\" height=\"167\" \/><br \/>\na. Write a polynomial that represents the perimeter of the blanket including the fringe.<br \/>\nb. Write a polynomial that represents the area of the blanket including the fringe.<br \/>\nc. Find the perimeter and the area of the blanket including the fringe when the width of the fringe is 4 inches.<br \/>\nAnswer:<br \/>\nLength = 72 + x + x<br \/>\n= 2x + 72<br \/>\nWidth = 48 + x + x<br \/>\n= 2x + 48<br \/>\nP = 2(l + w)<br \/>\nP = 2(120 + 4x)<br \/>\n= 240 + 8x<br \/>\nP = 8x + 240 in.<br \/>\nLength = 72 + x + x<br \/>\n= 2x + 72<br \/>\nWidth = 48 + x + x<br \/>\n= 2x + 48<br \/>\nA = lw<br \/>\nA = (72 + 2x)(48 + 2x)<br \/>\n= 4x\u00b2 + 120x + 3456<br \/>\nl = 72 + 4 + 4 = 80 in.<br \/>\nw = 48 + 4 + 4 = 56 in.<br \/>\nP = 2(l + w) = 2(80 + 56) = 272 in.<br \/>\nA = lw = 80 \u00d7 56 = 4480 sq. in<\/p>\n<p>Question 20.<br \/>\nYou are saving money to buy an electric guitar. You deposit $1000 in an account that earns interest compounded annually. The expression 1000(1 + r )<sup>2<\/sup> represents the balance after 2 years, where r is the annual interest rate in decimal form.<br \/>\na. Write the polynomial in a standard form that represents the balance of your account after 2 years.<br \/>\nb. The interest rate is 3%. What is the balance of your account after 2 years?<br \/>\nc. The guitar costs $1100. Do you have enough money in your account after 3 years? Explain.<br \/>\nAnswer:<br \/>\nA = P(1 + r\/2)<sup>nt<\/sup><br \/>\nA = 1000(1 + 0.03\/1)<sup>2<\/sup><br \/>\nA = 1000(1.03)\u00b2<br \/>\nA = P(1 + r\/2)<sup>nt<\/sup><br \/>\nA = 1000(1 + 0.03\/1)<sup>3<\/sup><br \/>\nA = 1000(1.03)\u00b2<br \/>\n1000(1\u00b2 + 2r + r\u00b2)<br \/>\n1000(1 + 2r + r\u00b2)<br \/>\n1000 + 2000r + 1000r\u00b2<br \/>\n1000r\u00b2 + 2000r + 1000<\/p>\n<p>Question 21.<br \/>\nThe front of a storage bunker can be modeled by y = &#8211; \\(\\frac{5}{216}\\)(x &#8211; 72)(x + 72), where x and y are measured in inches. The x-axis represents the ground. Find the width of the bunker at ground level.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36632\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-q-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring q 2\" width=\"280\" height=\"174\" \/><br \/>\nAnswer:<br \/>\ny = &#8211; \\(\\frac{5}{216}\\)(x &#8211; 72)(x + 72)<br \/>\n&#8211; \\(\\frac{5}{216}\\)(x &#8211; 72)(x + 72) = 0<br \/>\n(x &#8211; 72)(x + 72) = 0<br \/>\nx &#8211; 72 = 0 or x + 72 = 0<br \/>\nx = 72 or x = -72<br \/>\nx = 72, -72<\/p>\n<h3><a id=\"Lesson_7.5_Factoring_x2_+_bx_+_c\"><\/a>Lesson 7.5 Factoring x<sup>2<\/sup> + bx + c<\/h3>\n<p><strong>Essential Question<\/strong> How can you use algebra tiles to factor the trinomial x<sup>2<\/sup> + bx + c into the product of two binomials?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding Binomial Factors<br \/>\nWork with a partner. Use algebra tiles to write each polynomial as the product of two binomials. Check your answer by multiplying.<br \/>\nSample x<sup>2<\/sup> + 5x + 6<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36633\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 1\" width=\"536\" height=\"659\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-1.png 536w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-1-244x300.png 244w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Answer:<br \/>\na. x\u00b2 &#8211; 3x + 2<br \/>\n2 \u00d7 1 = 2<br \/>\nx\u00b2 &#8211; 1x &#8211; 2x + 2<br \/>\nx(x &#8211; 1) -2(x &#8211; 1)<br \/>\n(x &#8211; 1)(x &#8211; 2)<\/p>\n<p>b. x\u00b2 + 5x + 4<br \/>\nx\u00b2 + 1x + 4x + 4<br \/>\nx(x + 1) + 4(x + 1)<br \/>\n(x + 1)(x + 4)<\/p>\n<p>c. x\u00b2 &#8211; 7x + 12<br \/>\nx\u00b2 -4x &#8211; 3x + 12<br \/>\nx(x &#8211; 4) &#8211; 3(x &#8211; 4)<br \/>\n(x &#8211; 4)(x &#8211; 3)<\/p>\n<p>d. x\u00b2 + 7x + 12<br \/>\nx\u00b2 + 4x + 3x + 12<br \/>\nx(x + 4) + 3(x + 4)<br \/>\n(x + 4)(x + 3)<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nHow can you use algebra tiles to factor the trinomial x<sup>2<\/sup> + bx + c into the product of two binomials?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36634\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 2\" width=\"229\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n1. Arrange algebra tiles for the given trinomial x<sup>2<\/sup> + bx + c such that the model is a rectangular array.<br \/>\n2. Use additional algebra tiles to model the dimensions of the rectangle.<br \/>\n3. Write the polynomial in the factored form using the dimensions of the rectangle.<\/p>\n<p>Question 3.<br \/>\nDescribe a strategy for factoring the trinomial x<sup>2<\/sup> + bx + c that does not use algebra tiles.<br \/>\nAnswer: Finding the factors of the polynomial x<sup>2<\/sup> + bx + c.<\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> + 7x + 6<br \/>\nAnswer: x = -6, -1<\/p>\n<p>Explanation:<br \/>\nx\u00b2 + 7x + 6<br \/>\nx\u00b2 + 6x + 1x + 6<br \/>\nx(x + 6) + 1(x + 6)<br \/>\n(x + 6)(x + 1)<br \/>\nx + 6 = 0 or x + 1 = 0<br \/>\nx = -6, -1<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> + 9x + 8<br \/>\nAnswer: x = -1, -8<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> + 9x + 8<br \/>\nx\u00b2 + 1x + 8x + 8<br \/>\nx(x + 1) + 8(x + 1)<br \/>\n(x + 1)(x + 8)<br \/>\nx + 1 = 0 or x + 8 = 0<br \/>\nx = -1 or x = -8<br \/>\nx = -1, -8<\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 3.<br \/>\nw<sup>2<\/sup> &#8211; 4w + 3<br \/>\nAnswer: w = 3, 1<\/p>\n<p>Explanation:<br \/>\nw<sup>2<\/sup> &#8211; 4w + 3<br \/>\nw\u00b2 &#8211; 1w &#8211; 3w + 3<br \/>\nw(w &#8211; 1) &#8211; 3(w &#8211; 1)<br \/>\n(w &#8211; 3)(w &#8211; 1)<br \/>\nw &#8211; 3 = 0 or w &#8211; 1 = 0<br \/>\nw = 3, 1<\/p>\n<p>Question 4.<br \/>\nn<sup>2<\/sup> &#8211; 12n + 35<br \/>\nAnswer: n = 5, 7<\/p>\n<p>Explanation:<br \/>\nn<sup>2<\/sup> &#8211; 12n + 35<br \/>\nn\u00b2 &#8211; 7n &#8211; 5n + 35<br \/>\nn(n &#8211; 7) &#8211; 5(n &#8211; 7)<br \/>\n(n &#8211; 5)(n &#8211; 7)<br \/>\nn &#8211; 5 = 0 or n &#8211; 7 = 0<br \/>\nn = 5, 7<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> &#8211; 14x + 24<br \/>\nAnswer: x = 2, 12<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> &#8211; 14x + 24<br \/>\nx\u00b2 &#8211; 12x &#8211; 2x + 24<br \/>\nx(x &#8211; 12) -2(x &#8211; 12)<br \/>\n(x &#8211; 12)(x &#8211; 2)<br \/>\nx = 2, 12<\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> + 2x &#8211; 15<br \/>\nAnswer: x = 3, -5<\/p>\n<p>Explanation:<br \/>\nx<sup>2<\/sup> + 2x &#8211; 15<br \/>\nx\u00b2 + 5x &#8211; 3x &#8211; 15<br \/>\nx(x + 5) &#8211; 3(x + 5)<br \/>\n(x + 5)(x &#8211; 3)<br \/>\nx = 3, -5<\/p>\n<p>Question 7.<br \/>\ny<sup>2<\/sup> + 13y &#8211; 30<br \/>\nAnswer: y = 2, -15<\/p>\n<p>Explanation:<br \/>\ny<sup>2<\/sup> + 13y &#8211; 30<br \/>\ny\u00b2 + 15y &#8211; 2y &#8211; 30<br \/>\ny(y + 15) &#8211; 2(y + 15)<br \/>\n(y + 15)(y &#8211; 2)<br \/>\ny = 2, -15<\/p>\n<p>Question 8.<br \/>\nv<sup>2<\/sup> &#8211; v &#8211; 42<br \/>\nAnswer: v = 7, -6<\/p>\n<p>Explanation:<br \/>\nv<sup>2<\/sup> &#8211; v &#8211; 42<br \/>\nv\u00b2 &#8211; 7v + 6v &#8211; 42<br \/>\nv(v &#8211; 7) + 6(v &#8211; 7)<br \/>\n(v &#8211; 7)(v + 6)<br \/>\nv &#8211; 7 = 0 or v + 6 = 0<br \/>\nv = 7, -6<\/p>\n<p>Question 9.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe area of the pumpkin patch is 200 square meters. What is the area of the square plot of land?<br \/>\nAnswer:<br \/>\n200 = (s &#8211; 40)(s &#8211; 30)<br \/>\ns\u00b2 &#8211; 30s &#8211; 40s + 1200 = 200<br \/>\ns\u00b2 &#8211; 70s + 1000 = 0<br \/>\ns\u00b2 &#8211; 50s &#8211; 20s + 1000<br \/>\ns(s &#8211; 50) &#8211; 20(s &#8211; 50)<br \/>\n(s &#8211; 50)(s &#8211; 20) = 0<br \/>\ns &#8211; 50 = 0 or s &#8211; 20 = 0<br \/>\ns = 50 or 20<br \/>\n20 is less than 30 therefore the side of square is 50m.<br \/>\nArea of the plot = 50 \u00d7 50<br \/>\n= 2500 sq. meter<\/p>\n<h3><a id=\"Factoring_x2_+_bx_+_c_7.5_Exercises\"><\/a>Factoring x<sup>2<\/sup> + bx + c 7.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nYou are factoring x<sup>2<\/sup> + 11x = 26. What do the signs of the terms tell you about the factors? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44261\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 1\" width=\"513\" height=\"113\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-1.png 513w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-1-300x66.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a trinomial that can be factored as (x + p)(x + q), where p and q are positive.<br \/>\nAnswer:<br \/>\n(x + p)(x + q)<br \/>\nx\u00b2 + px + qx + pq<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, factor the polynomial.<\/strong><br \/>\nQuestion 3.<br \/>\nx<sup>2<\/sup> + 8x + 7<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44262\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 3\" width=\"324\" height=\"152\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-3.png 324w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-3-300x141.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Question 4.<br \/>\nz<sup>2<\/sup> + 10z + 21<br \/>\nAnswer:<br \/>\nz<sup>2<\/sup> + 7z + 3z + 21<br \/>\nz(z + 7) + 3(z + 7)<br \/>\n(z + 7)(z + 3)<br \/>\nz<sup>2<\/sup> + 10z + 21 = (z + 7)(z + 3)<\/p>\n<p>Question 5.<br \/>\nn<sup>2<\/sup> + 9n + 20<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44263\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 5\" width=\"459\" height=\"147\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-5.png 459w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-5-300x96.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 6.<br \/>\ns<sup>2<\/sup> + 11s + 30<br \/>\nAnswer:<br \/>\ns<sup>2<\/sup> + 11s + 30<br \/>\ns\u00b2 + 6s + 5s + 30<br \/>\ns(s + 6) + 5(s + 6)<br \/>\n(s + 6)(s + 5)<br \/>\ns<sup>2<\/sup> + 11s + 30 = (s + 6)(s + 5)<\/p>\n<p>Question 7.<br \/>\nh<sup>2<\/sup> + 11h + 18<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44264\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 7\" width=\"460\" height=\"149\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-7.png 460w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-7-300x97.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Question 8.<br \/>\ny<sup>2<\/sup> + 13y + 40<br \/>\nAnswer:<br \/>\ny<sup>2<\/sup> + 13y + 40<br \/>\ny\u00b2 + 8y + 5y + 40<br \/>\ny(y + 8) + 5(y + 8)<br \/>\n(y + 8)(y + 5)<br \/>\ny<sup>2<\/sup> + 13y + 40 = (y + 8)(y + 5)<\/p>\n<p><strong>In Exercises 9\u201314, factor the polynomial.<\/strong><br \/>\nQuestion 9.<br \/>\nv<sup>2<\/sup> &#8211; 5v + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44265\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 9\" width=\"366\" height=\"152\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-9.png 366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-9-300x125.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> &#8211; 13x + 22<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> &#8211; 13x + 22<br \/>\nx\u00b2 &#8211; 11x &#8211; 2x + 22<br \/>\nx(x &#8211; 11) -2(x &#8211; 11)<br \/>\n(x &#8211; 11)(x &#8211; 2)<br \/>\nx<sup>2<\/sup> &#8211; 13x + 22 = (x &#8211; 11)(x &#8211; 2)<\/p>\n<p>Question 11.<br \/>\nd<sup>2<\/sup> &#8211; 5d + 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44266\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 11\" width=\"403\" height=\"147\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-11.png 403w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-11-300x109.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 12.<br \/>\nk<sup>2<\/sup> &#8211; 10k + 24<br \/>\nAnswer:<br \/>\nk<sup>2<\/sup> &#8211; 10k + 24<br \/>\nk\u00b2 &#8211; 6k &#8211; 4k + 24<br \/>\nk(k &#8211; 6) -4(k &#8211; 6)<br \/>\n(k &#8211; 6)(k &#8211; 4)<br \/>\nk<sup>2<\/sup> &#8211; 10k + 24 = (k &#8211; 6)(k &#8211; 4)<\/p>\n<p>Question 13.<br \/>\nw<sup>2<\/sup> &#8211; 17w + 72<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44267\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 13\" width=\"581\" height=\"206\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-13.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-13-300x106.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 14.<br \/>\nj<sup>2<\/sup> &#8211; 13j + 42<br \/>\nAnswer:<br \/>\nj<sup>2<\/sup> &#8211; 13j + 42<br \/>\nj\u00b2 &#8211; 7j &#8211; 6j + 42<br \/>\nj(j &#8211; 7) -6(j &#8211; 7)<br \/>\n(j &#8211; 7)(j &#8211; 6)<br \/>\nj<sup>2<\/sup> &#8211; 13j + 42 = (j &#8211; 7)(j &#8211; 6)<\/p>\n<p><strong>In Exercises 15\u201324, factor the polynomial.<\/strong><br \/>\nQuestion 15.<br \/>\nx<sup>2<\/sup> + 3x &#8211; 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44268\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 15\" width=\"485\" height=\"152\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-15.png 485w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-15-300x94.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 16.<br \/>\nz<sup>2<\/sup> + 7z &#8211; 18<br \/>\nAnswer:<br \/>\nz<sup>2<\/sup> + 7z &#8211; 18<br \/>\nz\u00b2 + 9z &#8211; 2z &#8211; 18<br \/>\nz(z + 9) &#8211; 2(z + 9)<br \/>\n(z + 9)(z &#8211; 2)<br \/>\nz<sup>2<\/sup> + 7z &#8211; 18 = (z + 9)(z &#8211; 2)<\/p>\n<p>Question 17.<br \/>\nn<sup>2<\/sup> + 4n &#8211; 12<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44269\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 17\" width=\"581\" height=\"211\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-17.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-17-300x109.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 18.<br \/>\ns<sup>2<\/sup> + 3s &#8211; 40<br \/>\nAnswer:<br \/>\ns<sup>2<\/sup> + 3s &#8211; 40<br \/>\ns\u00b2 + 8s &#8211; 5s &#8211; 40<br \/>\ns(s + 8) &#8211; 5(s + 8)<br \/>\n(s &#8211; 5)(s + 8)<br \/>\ns<sup>2<\/sup> + 3s &#8211; 40 = (s &#8211; 5)(s + 8)<\/p>\n<p>Question 19.<br \/>\ny<sup>2<\/sup> + 2y &#8211; 48<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44270\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 19\" width=\"587\" height=\"205\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-19.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-19-300x105.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 20.<br \/>\nh<sup>2<\/sup> + 6h &#8211; 27<br \/>\nAnswer:<br \/>\nh<sup>2<\/sup> + 6h &#8211; 27<br \/>\nh\u00b2 + 9h &#8211; 3h &#8211; 27 = 0<br \/>\nh(h + 9) &#8211; 3(h + 9) = 0<br \/>\n(h + 9)(h &#8211; 3) = 0<br \/>\nh<sup>2<\/sup> + 6h &#8211; 27 = (h + 9)(h &#8211; 3)<\/p>\n<p>Question 21.<br \/>\nx<sup>2<\/sup> &#8211; x &#8211; 20<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44271\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 21\" width=\"585\" height=\"207\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-21.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-21-300x106.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 22.<br \/>\nm<sup>2<\/sup> &#8211; 6m &#8211; 7<br \/>\nAnswer:<br \/>\nm<sup>2<\/sup> &#8211; 6m &#8211; 7<br \/>\nm\u00b2 &#8211; 7m + 1m &#8211; 7 = 0<br \/>\nm(m &#8211; 7) + 1(m &#8211; 7) = 0<br \/>\n(m &#8211; 7)(m + 1) = 0<br \/>\nm = 7, -1<\/p>\n<p>Question 23.<br \/>\n-6t &#8211; 16 + t<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44272\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 23\" width=\"577\" height=\"212\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-23.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-23-300x110.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 24.<br \/>\n-7y + y<sup>2<\/sup> &#8211; 30<br \/>\nAnswer:<br \/>\n-7y + y<sup>2<\/sup> &#8211; 30<br \/>\ny\u00b2 &#8211; 7y &#8211; 30 = 0<br \/>\ny\u00b2 &#8211; 10y + 3y &#8211; 30 = 0<br \/>\ny(y &#8211; 10) + 3(y &#8211; 10) = 0<br \/>\n(y + 3)(y &#8211; 10) = 0<br \/>\ny = -3, 10<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA projector displays an image on a wall. The area (in square feet) of the projection is represented by x<sup>2<\/sup> &#8211; 8x + 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36635\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 3\" width=\"161\" height=\"156\" \/><br \/>\na. Write a binomial that represents the height of the projection.<br \/>\nb. Find the perimeter of the projection when the height of the wall is 8 feet.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44273\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 25\" width=\"552\" height=\"456\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-25.png 552w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-25-300x248.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA dentist\u2019s office and parking lot are on a rectangular piece of land. The area (in square meters) of the land is represented by x<sup>2<\/sup> + x &#8211; 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36636\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-4.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 4\" width=\"274\" height=\"151\" \/><br \/>\na. Write a binomial that represents the width of the land.<br \/>\nb. Find the area of the land when the length of the dentist\u2019s office is 20 meters.<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> + x &#8211; 30<br \/>\nx\u00b2 + 6x &#8211; 5x &#8211; 30 = 0<br \/>\nx(x + 6) &#8211; 5(x + 6) = 0<br \/>\n(x + 6)(x &#8211; 5) = 0<br \/>\nx = -6, 5<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 27 and 28, describe and correct the error in factoring the polynomial.<br \/>\nQuestion 27.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36637\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 5\" width=\"320\" height=\"79\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-5.png 320w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-5-300x74.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44274\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 27\" width=\"577\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-27.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-27-300x101.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 28.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36638\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-6.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 6\" width=\"323\" height=\"79\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-6.png 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-6-300x73.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nAnswer:<br \/>\ns\u00b2 &#8211; 17s &#8211; 60 = 0<br \/>\ns\u00b2 &#8211; 20s + 3s &#8211; 60 = 0<br \/>\ns(s &#8211; 20) + 3(s &#8211; 20) = 0<br \/>\n(s &#8211; 20)(s + 3) = 0<br \/>\ns = -3, 20<\/p>\n<p><strong>In Exercises 29\u201338, solve the equation.<\/strong><br \/>\nQuestion 29.<br \/>\nm<sup>2<\/sup> + 3m + 2 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44275\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 29\" width=\"475\" height=\"318\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-29.png 475w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-29-300x201.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 30.<br \/>\nn<sup>2<\/sup> &#8211; 9n + 18 = 0<br \/>\nAnswer:<br \/>\nn<sup>2<\/sup> &#8211; 9n + 18 = 0<br \/>\nn\u00b2 &#8211; 6n &#8211; 3n + 18 = 0<br \/>\nn(n &#8211; 6) -3(n &#8211; 6) = 0<br \/>\n(n &#8211; 3)(n &#8211; 6) = 0<br \/>\nn = 3, 6<\/p>\n<p>Question 31.<br \/>\nx<sup>2<\/sup> + 5x &#8211; 14 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44276\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 31\" width=\"559\" height=\"308\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-31.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-31-300x165.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 32.<br \/>\nv<sup>2<\/sup> + 11v &#8211; 26 = 0<br \/>\nAnswer:<br \/>\nv<sup>2<\/sup> + 11v &#8211; 26 = 0<br \/>\nv\u00b2 + 13v &#8211; 2v &#8211; 26 = 0<br \/>\nv(v + 13) &#8211; 2(v + 13) = 0<br \/>\n(v + 13)(v &#8211; 2) = 0<br \/>\nv = -13, 2<\/p>\n<p>Question 33.<br \/>\nt<sup>2<\/sup> + 15t = -36<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44277\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 33\" width=\"519\" height=\"362\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-33.png 519w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-33-300x209.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 34.<br \/>\nn<sup>2<\/sup> &#8211; 5n = 24<br \/>\nAnswer:<br \/>\nn\u00b2 &#8211; 5n = 24<br \/>\nn\u00b2 &#8211; 5n &#8211; 24 = 0<br \/>\nn\u00b2 &#8211; 8n + 3n &#8211; 24 = 0<br \/>\nn(n &#8211; 8) + 3(n &#8211; 8) = 0<br \/>\n(n &#8211; 8)(n + 3) = 0<br \/>\nn &#8211; 8 = 0 or n + 3 = 0<br \/>\nn = 8 or n = -3<br \/>\nn = -3, 8<\/p>\n<p>Question 35.<br \/>\na<sup>2<\/sup> + 5a &#8211; 20 = 30<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44278\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 35\" width=\"511\" height=\"412\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-35.png 511w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-35-300x242.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 36.<br \/>\ny<sup>2<\/sup> &#8211; 2y &#8211; 8 = 7<br \/>\nAnswer:<br \/>\ny<sup>2<\/sup> &#8211; 2y &#8211; 8 = 7<br \/>\ny\u00b2 &#8211; 2y &#8211; 8 &#8211; 7 = 0<br \/>\ny\u00b2 &#8211; 2y &#8211; 15 = 0<br \/>\ny\u00b2 &#8211; 5y + 3y &#8211; 15 = 0<br \/>\ny(y &#8211; 5) + 3(y &#8211; 5) = 0<br \/>\n(y &#8211; 5)(y + 3) = 0<br \/>\ny &#8211; 5 = 0 or y + 3 = 0<br \/>\ny = 5, -3<\/p>\n<p>Question 37.<br \/>\nm<sup>2<\/sup> + 10 = 15m &#8211; 34<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44279\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 37\" width=\"511\" height=\"448\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-37.png 511w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-37-300x263.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 38.<br \/>\nb<sup>2<\/sup> + 5 = 8b &#8211; 10<br \/>\nAnswer:<br \/>\nb<sup>2<\/sup> + 5 = 8b &#8211; 10<br \/>\nb\u00b2 + 5 &#8211; 8b + 10 = 0<br \/>\nb\u00b2 &#8211; 8b + 15 = 0<br \/>\nb\u00b2 &#8211; 3b &#8211; 5b + 15 = 0<br \/>\nb(b &#8211; 3) -5(b &#8211; 3) = 0<br \/>\n(b &#8211; 3)(b &#8211; 5)<br \/>\nb &#8211; 3 = 0 or b &#8211; 5 = 0<br \/>\nb = 3, 5<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou trimmed a large square picture so that you could fit it into a frame. The area of the cut picture is 20 square inches. What is the area of the original picture?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36639\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 7\" width=\"218\" height=\"191\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44280\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-39.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 39.1\" width=\"574\" height=\"339\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-39.1.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-39.1-300x177.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44281\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-39.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 39.2\" width=\"557\" height=\"379\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-39.2.png 557w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-39.2-300x204.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA web browser is open on your computer screen.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36640\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-8.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 8\" width=\"194\" height=\"156\" \/><br \/>\na. The area of the browser window is 24 square inches. Find the length of the browser window x.<br \/>\nb. The browser covers \\(\\frac{3}{13}\\) of the screen. What are the dimensions of the screen?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe area of the browser window is 24 square inches.<br \/>\nx\u00b2 = 24 in\u00b2<br \/>\nx = \u221a24 = 4.9 in.<br \/>\nA = \\(\\frac{3}{13}\\) \u00d7 24 = 104 sq. in.<br \/>\ns\\(\\frac{3}{13}\\) = 104 in\\(\\frac{3}{13}\\)<br \/>\ns = \u221a(104 in\u00b2) = 10.2 in.<\/p>\n<p>Question 41.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says there are six integer values of b for which the trinomial x<sup>2<\/sup> + bx &#8211; 12 has two binomial factors of the form (x + p) and (x + q). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44282\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 41\" width=\"577\" height=\"326\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-41.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-41-300x169.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse algebra tiles to factor each polynomial modeled by the tiles. Show your work.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36641\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 9\" width=\"264\" height=\"123\" \/><br \/>\nAnswer:<br \/>\na. x\u00b2 &#8211; x &#8211; 6 = x\u00b2 &#8211; 3x + 2x &#8211; 6<br \/>\n= x(x &#8211; 3) + 2(x &#8211; 3)<br \/>\n= (x + 2)(x &#8211; 3)<\/p>\n<p>b. x\u00b2 + 2x &#8211; 8<br \/>\n= x\u00b2 + 4x &#8211; 2x &#8211; 8<br \/>\n= x(x + 4) &#8211; 2(x + 4)<br \/>\n= (x + 4)(x &#8211; 2)<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 43 and 44, find the dimensions of the polygon with the given area.<br \/>\nQuestion 43.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36642\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-10.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 10\" width=\"190\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44283\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 43\" width=\"589\" height=\"601\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-43.png 589w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-43-294x300.png 294w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 44.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36643\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 11\" width=\"187\" height=\"133\" \/><br \/>\nAnswer:<br \/>\nA = lw<br \/>\n35 = (g &#8211; 11)(g &#8211; 8)<br \/>\n35 = g(g &#8211; 8) &#8211; 11(g &#8211; 8)<br \/>\n35 = g\u00b2 &#8211; 8g &#8211; 11g + 88<br \/>\n35 = g\u00b2 &#8211; 19g + 88<br \/>\ng\u00b2 &#8211; 19g + 88 &#8211; 35 = 0<br \/>\ng\u00b2 &#8211; 19g + 53 = 0<\/p>\n<p>Question 45.<br \/>\n<strong>REASONING<\/strong><br \/>\nWrite an equation of the form x<sup>2<\/sup> + bx + c = 0 that has the solutions x = -4 and x = 6. Explain how you found your answer.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44284\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 45\" width=\"582\" height=\"257\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-45.png 582w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-45-300x132.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph of y = x<sup>2<\/sup> + x &#8211; 6 is shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36644\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-12.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 12\" width=\"211\" height=\"168\" \/><br \/>\na. Explain how you can use the graph to factor the polynomial x<sup>2<\/sup> + x &#8211; 6.<br \/>\nb. Factor the polynomial.<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> + x &#8211; 6<br \/>\nx\u00b2 + 3x &#8211; 2x &#8211; 6<br \/>\nx(x + 3) &#8211; 2(x + 3)<br \/>\n(x + 3)(x &#8211; 2)<br \/>\nx = -3, 2<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nRoad construction workers are paving the area shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36645\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.5-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.5 13\" width=\"195\" height=\"158\" \/><br \/>\na. Write an expression that represents the area being paved.<br \/>\nb. The area being paved is 280 square meters. Write and solve an equation to find the width of the road x.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44285\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 47.1\" width=\"527\" height=\"314\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.1.png 527w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.1-300x179.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44286\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 47.2\" width=\"595\" height=\"408\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.2.png 595w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.2-300x206.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44287\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 47.3\" width=\"589\" height=\"263\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.3.png 589w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-47.3-300x134.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 48\u201351, factor the polynomial.<br \/>\nQuestion 48.<br \/>\nx<sup>2<\/sup> + 6xy + 8y<sup>2<\/sup><br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> + 6xy + 8y\u00b2<br \/>\nx\u00b2 + 4xy + 2xy + 4y\u00b2<br \/>\nx(x + 4y) + 2y(x + 4y)<br \/>\n(x + 4y)(x + 2y)<\/p>\n<p>Question 49.<br \/>\nr<sup>2<\/sup> + 7rs + 12s<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44288\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 49\" width=\"378\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-49.png 378w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-49-300x119.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 50.<br \/>\na<sup>2<\/sup> + 11ab &#8211; 26b<sup>2<\/sup><br \/>\nAnswer:<br \/>\na<sup>2<\/sup> + 11ab &#8211; 26b<sup>2<\/sup><br \/>\nFactors of 26 are (1, 26), (2, 13)<br \/>\nSum of factors 13 &#8211; 2 = 11<br \/>\na<sup>2<\/sup> + 11ab &#8211; 26b\u00b2<br \/>\n= a\u00b2 + 13ab &#8211; 2ab &#8211; 26b\u00b2<br \/>\n= a(a + 13b) &#8211; 2b(a + 13b)<br \/>\n= (a + 13b)(a &#8211; 2b)<\/p>\n<p>Question 51.<br \/>\nx<sup>2<\/sup> &#8211; 2xy &#8211; 35y<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44289\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 51\" width=\"531\" height=\"161\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-51.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-51-300x91.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 52.<br \/>\np &#8211; 9 = 0<br \/>\nAnswer:<br \/>\nGiven,<br \/>\np &#8211; 9 = 0<br \/>\np = 0 + 9<br \/>\np = 9<\/p>\n<p>Question 53.<br \/>\nz + 12 = -5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44290\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 53\" width=\"448\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-53.png 448w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-53-300x91.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p>Question 54.<br \/>\n6 = \\(\\frac{c}{-7}\\)<br \/>\nAnswer:<br \/>\n6 = \\(\\frac{c}{-7}\\)<br \/>\n6 \u00d7 -7 = c<br \/>\nc = -42<\/p>\n<p>Question 55.<br \/>\n4k = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44291\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.5 Question 55\" width=\"326\" height=\"145\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-55.png 326w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.5-Question-55-300x133.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<h3><a id=\"Lesson_7.6_Factoring_ax2_+_bx_+_c\"><\/a>Lesson 7.6 Factoring ax<sup>2<\/sup> + bx + c<\/h3>\n<p><strong>Essential Question<\/strong> How can you use algebra tiles to factor the trinomial ax<sup>2<\/sup> + bx + c into the product of two binomials?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Finding Binomial Factors<br \/>\nWork with a partner. Use algebra tiles to write each polynomial as the product of two binomials. Check your answer by multiplying.<br \/>\nSample 2x<sup>2<\/sup> + 5x + 2<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36647\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 1\" width=\"506\" height=\"669\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-1.png 506w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-1-227x300.png 227w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Answer:<br \/>\na. 3x\u00b2 + 5x + 2<br \/>\n3x\u00b2 + 5x + 2 = 3x\u00b2 + 3x + 2x + 2<br \/>\n= 3x(x + 1) + 2(x + 1)<br \/>\n= (x + 1)(3x + 2)<\/p>\n<p>b. 4x\u00b2 + 4x &#8211; 3 = (2x + 3)(2x &#8211; 1)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-195681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Lesson-7.6-Factoring-ax2-bx-c_1b.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Lesson 7.6 Factoring ax2 + bx + c_1b\" width=\"190\" height=\"250\" \/><br \/>\nCheck:<br \/>\n(2x + 3)(2x &#8211; 1) = 4x\u00b2 &#8211; 2x + 6x &#8211; 3<br \/>\n= 4x\u00b2 + 4x &#8211; 3<\/p>\n<p>c.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-195679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Lesson-7.6-Factoring-ax2-bx-c_1c.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Lesson 7.6 Factoring ax2 + bx + c_1c\" width=\"208\" height=\"234\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-195680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Lesson-7.6-Factoring-ax2-bx-c_1c_2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Lesson 7.6 Factoring ax2 + bx + c_1c_2\" width=\"190\" height=\"238\" \/><br \/>\n2x\u00b2 &#8211; 11x + 5 = (x &#8211; 5)(2x &#8211; 1)<br \/>\nBy checking<br \/>\n(x &#8211; 5)(2x &#8211; 1) = 2x\u00b2 &#8211; x &#8211; 10x + 5<br \/>\n= 2x\u00b2 &#8211; 11x + 5<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nHow can you use algebra tiles to factor the trinomial ax<sup>2<\/sup> + bx + c into the product of two binomials?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36648\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 2\" width=\"219\" height=\"183\" \/><br \/>\nAnswer:<br \/>\nIf the value of c is negative, you would need zero pairs to model the factorization of the polynomial. The x-tiles on the board determine what the constants are in the factors. The product of these constants is equal to the value of c, so you would need positive tiles on one side of the x-squared tile and negative x-tiles on the other side to have opposite signs on the constants. Opposite signs on the constants will result in a negative value for c when multiplying the factors.<\/p>\n<p>Question 3.<br \/>\nIs it possible to factor the trinomial 2x<sup>2<\/sup> + 2x + 1? Explain your reasoning.<br \/>\nAnswer: No, it is not possible to factor the trinomial 2x<sup>2<\/sup> + 2x + 1. Because it does not have the factors.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 1.<br \/>\n8x<sup>2<\/sup> &#8211; 56x + 48<br \/>\nAnswer:<br \/>\n8x<sup>2<\/sup> &#8211; 56x + 48<br \/>\n= 8(x\u00b2 &#8211; 7x + 6)<br \/>\n= 8(x\u00b2- 1x &#8211; 6x + 6)<br \/>\n= 8[x(x &#8211; 1) &#8211; 6(x &#8211; 1)]<br \/>\n= 8[(x- 1)(x &#8211; 6)]<\/p>\n<p>Question 2.<br \/>\n14x<sup>2<\/sup> + 31x + 15<br \/>\nAnswer:<br \/>\n14x<sup>2<\/sup> + 31x + 15<br \/>\n14x\u00b2 + 21x + 10x + 15<br \/>\n7x(2x + 3) + 5(2x + 3)<br \/>\n(7x + 5)(2x + 3)<\/p>\n<p>Question 3.<br \/>\n2x<sup>2<\/sup> &#8211; 7x + 5<br \/>\nAnswer:<br \/>\n2x<sup>2<\/sup> &#8211; 7x + 5<br \/>\n2x\u00b2 &#8211; 2x &#8211; 5x + 5<br \/>\n2x(x &#8211; 1) -5(x &#8211; 1)<br \/>\n(x &#8211; 1)(2x &#8211; 5)<\/p>\n<p>Question 4.<br \/>\n3x<sup>2<\/sup> &#8211; 14x + 8<br \/>\nAnswer:<br \/>\n3x<sup>2<\/sup> &#8211; 14x + 8<br \/>\n3x\u00b2 &#8211; 12x &#8211; 2x + 8<br \/>\n3x(x &#8211; 4) &#8211; 2(x &#8211; 4)<br \/>\n(x &#8211; 4)(3x &#8211; 2)<\/p>\n<p>Question 5.<br \/>\n4x<sup>2<\/sup> &#8211; 19x &#8211; 5<br \/>\nAnswer:<br \/>\n4x<sup>2<\/sup> &#8211; 19x &#8211; 5<br \/>\n4x\u00b2 -20x + 1x &#8211; 5<br \/>\n4x(x &#8211; 5) + 1(x &#8211; 5)<br \/>\n(x &#8211; 5)(4x + 1)<\/p>\n<p>Question 6.<br \/>\n6x<sup>2<\/sup> + x &#8211; 12<br \/>\nAnswer:<br \/>\n6x<sup>2<\/sup> + x &#8211; 12<br \/>\n6x\u00b2 + 9x &#8211; 8x &#8211; 12<br \/>\n3x(2x + 3) -4(2x + 3)<br \/>\n(2x + 3)(3x &#8211; 4)<\/p>\n<p>Question 7.<br \/>\n-2y<sup>2<\/sup> &#8211; 5y &#8211; 3<br \/>\nAnswer:<br \/>\n-2y<sup>2<\/sup> &#8211; 5y &#8211; 3<br \/>\n-2y\u00b2 &#8211; 2y &#8211; 3y &#8211; 3<br \/>\n-2y(y + 1) &#8211; 3(y + 1)<br \/>\n(y + 1)(-2y &#8211; 3)<\/p>\n<p>Question 8.<br \/>\n-5m<sup>2<\/sup> + 6m &#8211; 1<br \/>\nAnswer:<br \/>\n-5m<sup>2<\/sup> + 6m &#8211; 1<br \/>\n-5m\u00b2 + 5m + 1m &#8211; 1<br \/>\n-5m(m &#8211; 1) + 1(m &#8211; 1)<br \/>\n(m &#8211; 1)(-5m + 1)<\/p>\n<p>Question 9.<br \/>\n-3x<sup>2<\/sup> &#8211; x + 2<br \/>\nAnswer:<br \/>\n-3x<sup>2<\/sup> &#8211; x + 2<br \/>\n-3x\u00b2 &#8211; 3x + 2x + 2<br \/>\n-3x(x + 1) + 2(x + 1)<br \/>\n(x + 1)(-3x + 2)<\/p>\n<p>Question 10.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe area of the reserve is 136 square miles. How wide is the reserve?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThe area of the reserve is 136 square miles.<br \/>\nA = w(2w + 1)<br \/>\n136 = w(2w + 1)<br \/>\n2w\u00b2 + w = 136<br \/>\n2w\u00b2 + w &#8211; 136 = 0<br \/>\n2w\u00b2 + 17w &#8211; 16w &#8211; 136 = 0<br \/>\nw(2w + 17) &#8211; 8(2w + 17) = 0<br \/>\n(w &#8211; 8)(2w + 17) = 0<br \/>\nw &#8211; 8 = 0 or 2w + 17 = 0<br \/>\nw = 8 or 2w = -17<br \/>\nw = 8 or w = -17\/2<\/p>\n<h3><a id=\"Factoring_ax2_+_bx_+_c_7.6_Exercises\"><\/a>Factoring ax<sup>2<\/sup> + bx + c 7.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat is the greatest common factor of the terms of 3y<sup>2<\/sup> &#8211; 21y + 36?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44292\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 1\" width=\"411\" height=\"60\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-1.png 411w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-1-300x44.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare factoring 6x<sup>2<\/sup> &#8211; x &#8211; 2 with factoring x<sup>2<\/sup> &#8211; x &#8211; 2.<br \/>\nAnswer:<br \/>\n6x<sup>2<\/sup> &#8211; x &#8211; 2 = 6x\u00b2 &#8211; 12x + 1x &#8211; 2<br \/>\n= 6x(x &#8211; 2) + 1(x &#8211; 2)<br \/>\n= (6x + 1)(x &#8211; 2)<br \/>\nx\u00b2 &#8211; x &#8211; 2 = x\u00b2 &#8211; 2x + 1x &#8211; 2<br \/>\n= x(x &#8211; 2) + 1(x &#8211; 2)<br \/>\n(x &#8211; 2)(x + 1)<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, factor the polynomial.<\/strong><br \/>\nQuestion 3.<br \/>\n3x<sup>2<\/sup> + 3x &#8211; 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44294\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 3\" width=\"366\" height=\"191\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-3.png 366w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-3-300x157.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><\/p>\n<p>Question 4.<br \/>\n8v<sup>2<\/sup> + 8v &#8211; 48<br \/>\nAnswer:<br \/>\n8v\u00b2 + 8v &#8211; 48<br \/>\n8(v\u00b2 + v &#8211; 6)<br \/>\n8[v\u00b2 + 3v &#8211; 2v &#8211; 6]<br \/>\n8[v(v + 3) &#8211; 2(v + 3)]<br \/>\n8[(v + 3)(v &#8211; 2)]<br \/>\n8v\u00b2 + 8v &#8211; 48 = 8[(v + 3)(v &#8211; 2)]<\/p>\n<p>Question 5.<br \/>\n4k<sup>2<\/sup> + 28k + 48<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44295\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 5\" width=\"463\" height=\"186\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-5.png 463w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-5-300x121.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 6.<br \/>\n6y<sup>2<\/sup> &#8211; 24y + 18<br \/>\nAnswer:<br \/>\n6y\u00b2 &#8211; 24y + 18<br \/>\n6[y\u00b2 &#8211; 4y + 3]<br \/>\n= 6[y\u00b2 &#8211; 3y &#8211; 1y + 3]<br \/>\n= 6[y(y &#8211; 3) &#8211; 1(y &#8211; 3)]<br \/>\n= 6[(y &#8211; 3) (y &#8211; 1)]<\/p>\n<p>Question 7.<br \/>\n7b<sup>2<\/sup> &#8211; 63b + 140<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44296\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 7\" width=\"505\" height=\"188\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-7.png 505w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-7-300x112.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 8.<br \/>\n9r<sup>2<\/sup> &#8211; 36r &#8211; 45<br \/>\nAnswer:<br \/>\n9r\u00b2 &#8211; 36r &#8211; 45<br \/>\n= 9[r\u00b2 &#8211; 4r &#8211; 5]<br \/>\n= 9[r\u00b2 &#8211; 5r + 1r &#8211; 5]<br \/>\n= 9[r(r &#8211; 5) + 1(r &#8211; 5)]<br \/>\n= 9[(r &#8211; 5)(r + 1)]<\/p>\n<p><strong>In Exercises 9\u201316, factor the polynomial.<\/strong><br \/>\nQuestion 9.<br \/>\n3h<sup>2<\/sup> + 11h + 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44298\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 9\" width=\"581\" height=\"392\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-9.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-9-300x202.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 10.<br \/>\n8m<sup>2<\/sup> + 30m + 7<br \/>\nAnswer:<br \/>\n8m\u00b2 + 30m + 7<br \/>\n= 8m\u00b2 + 28m + 2m + 7<br \/>\n= 4m(2m + 7) + 1(2m + 7)<br \/>\n= (2m + 7)(4m + 1)<\/p>\n<p>Question 11.<br \/>\n6x<sup>2<\/sup> &#8211; 5x + 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44299\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 11\" width=\"575\" height=\"283\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-11.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-11-300x148.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 12.<br \/>\n10w<sup>2<\/sup> &#8211; 31w + 15<br \/>\nAnswer:<br \/>\n10w\u00b2 &#8211; 31w + 15<br \/>\n10w\u00b2 &#8211; 25w &#8211; 6w + 15<br \/>\n5w(2w &#8211; 5) &#8211; 3(2w &#8211; 5)<br \/>\n(2w &#8211; 5)(5w &#8211; 3)<br \/>\n10w\u00b2 &#8211; 31w + 15 = (2w &#8211; 5)(5w &#8211; 3)<\/p>\n<p>Question 13.<br \/>\n3n<sup>2<\/sup> + 5n &#8211; 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44300\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 13\" width=\"584\" height=\"404\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-13.png 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-13-300x208.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 14.<br \/>\n4z<sup>2<\/sup> + 4z &#8211; 3<br \/>\nAnswer:<br \/>\n4z\u00b2 + 4z &#8211; 3<br \/>\n4z\u00b2 + 6z &#8211; 2z &#8211; 3<br \/>\n2z(2z + 3) &#8211; 1(2z + 3)<br \/>\n(2z &#8211; 1)(2x + 3)<\/p>\n<p>Question 15.<br \/>\n8g<sup>2<\/sup> &#8211; 10g &#8211; 12<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44301\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 15.1\" width=\"334\" height=\"34\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.1.png 334w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.1-300x31.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44302\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 15.2\" width=\"572\" height=\"577\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.2.png 572w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.2-297x300.png 297w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.2-150x150.png 150w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44303\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 15.3\" width=\"575\" height=\"301\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.3.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-15.3-300x157.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 16.<br \/>\n18v<sup>2<\/sup> &#8211; 15v &#8211; 18<br \/>\nAnswer:<br \/>\n18v\u00b2 &#8211; 15v &#8211; 18<br \/>\n= 3(6v\u00b2 &#8211; 5v &#8211; 6)<br \/>\n= 3[6v\u00b2 &#8211; 9v + 4v &#8211; 6]<br \/>\n= 3[3v(2v &#8211; 3) + 2(2v &#8211; 3)]<br \/>\n= 3[(2v &#8211; 3)(3v + 2)]<\/p>\n<p><strong>In Exercises 17\u201322, factor the polynomial.<\/strong><br \/>\nQuestion 17.<br \/>\n-3t<sup>2<\/sup> + 11t &#8211; 6<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44304\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 17\" width=\"585\" height=\"410\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-17.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-17-300x210.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 18.<br \/>\n-7v<sup>2<\/sup> &#8211; 25v &#8211; 12<br \/>\nAnswer:<br \/>\n-7v\u00b2 &#8211; 25v &#8211; 12<br \/>\n= -7v\u00b2 &#8211; 7v &#8211; 12v &#8211; 12<br \/>\n= -7v(v + 1) &#8211; 12(v + 1)<br \/>\n= (v + 1)(-7v &#8211; 12)<\/p>\n<p>Question 19.<br \/>\n-4c<sup>2<\/sup> + 19c + 5<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44305\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 19\" width=\"581\" height=\"511\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-19.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-19-300x264.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 20.<br \/>\n-8h<sup>2<\/sup> &#8211; 13h + 6<br \/>\nAnswer:<br \/>\n-8h\u00b2 &#8211; 13n + 6<br \/>\n= -8h\u00b2 &#8211; 16n + 3n + 6<br \/>\n= -8h(h + 2) + 3(h + 2)<br \/>\n= (h + 2)(-8h + 3)<\/p>\n<p>Question 21.<br \/>\n-15w<sup>2<\/sup> &#8211; w + 28<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44306\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 21.1\" width=\"489\" height=\"572\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.1.png 489w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.1-256x300.png 256w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44307\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 21.2\" width=\"495\" height=\"636\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.2.png 495w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.2-233x300.png 233w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44308\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 21.3\" width=\"480\" height=\"78\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.3.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-21.3-300x49.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>Question 22.<br \/>\n-22d<sup>2<\/sup> + 29d &#8211; 9<br \/>\nAnswer:<br \/>\n-22d\u00b2 + 29d &#8211; 9<br \/>\n= -22d\u00b2 + 11d + 18d &#8211; 9<br \/>\n= -11d(2d &#8211; 1) + 9(2d &#8211; 1)<br \/>\n= (-11d + 9)(2d &#8211; 1)<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 23 and 24, describe and correct the error in factoring the polynomial.<br \/>\nQuestion 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36649\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 3\" width=\"319\" height=\"80\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-3.png 319w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-3-300x75.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44309\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 23\" width=\"620\" height=\"294\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-23.png 620w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-23-300x142.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36650\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 4\" width=\"328\" height=\"70\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-4.png 328w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-4-300x64.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\n6x\u00b2 &#8211; 7x &#8211; 3<br \/>\n= 6x\u00b2 &#8211; 9x + 2x &#8211; 3<br \/>\n= 3x(2x &#8211; 3) + 1(2x &#8211; 3)<br \/>\n= (2x &#8211; 3)(3x + 1)<\/p>\n<p><strong>In Exercises 25\u201328, solve the equation.<\/strong><br \/>\nQuestion 25.<br \/>\n5x<sup>2<\/sup> &#8211; 5x &#8211; 30 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44310\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 25\" width=\"545\" height=\"424\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-25.png 545w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-25-300x233.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 26.<br \/>\n2k<sup>2<\/sup> &#8211; 5k &#8211; 18 = 0<br \/>\nAnswer:<br \/>\n2k\u00b2 &#8211; 5k &#8211; 18 = 0<br \/>\n= 2k\u00b2 + 4k &#8211; 9k &#8211; 18 = 0<br \/>\n= 2k(k + 2) &#8211; 9(k + 2) = 0<br \/>\n= (2k &#8211; 9)(k + 2) = 0<br \/>\n2k &#8211; 9 = 0 or k + 2 = 0<br \/>\n2k = 9 or k = -2<br \/>\nk = 9\/2<br \/>\nk = 9\/2, -2<\/p>\n<p>Question 27.<br \/>\n-12n<sup>2<\/sup> &#8211; 11n = -15<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44311\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 27.1\" width=\"805\" height=\"585\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.1.png 805w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.1-300x218.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.1-768x558.png 768w\" sizes=\"(max-width: 805px) 100vw, 805px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44312\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 27.2\" width=\"700\" height=\"609\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.2.png 700w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.2-300x261.png 300w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44313\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 27.3\" width=\"613\" height=\"101\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.3.png 613w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-27.3-300x49.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p>Question 28.<br \/>\n14b<sup>2<\/sup> &#8211; 2 = -3b<br \/>\nAnswer:<br \/>\n14b\u00b2 &#8211; 2 = -3b<br \/>\n= 14b\u00b2 &#8211; 2 + 3b = 0<br \/>\n= 14b\u00b2 + 3b &#8211; 2 = 0<br \/>\n= 14b\u00b2 + 7b &#8211; 4b &#8211; 2 = 0<br \/>\n= 7b(2b + 1) &#8211; 2(2b + 1) = 0<br \/>\n(2b + 1)(7b &#8211; 2) = 0<br \/>\n2b + 1 = 0 or 7b &#8211; 2 = 0<br \/>\n2b = -1 or 7b = 2<br \/>\nb = -1\/2 or b = 2\/7<br \/>\nb = -1\/2, 2\/7<\/p>\n<p><strong>In Exercises 29\u201332, find the x-coordinates of the points where the graph crosses the x-axis.<\/strong><br \/>\nQuestion 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36651\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 5\" width=\"144\" height=\"183\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44314\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-29.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 29.1\" width=\"576\" height=\"611\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-29.1.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-29.1-283x300.png 283w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44315\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-29.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 29.2\" width=\"593\" height=\"406\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-29.2.png 593w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-29.2-300x205.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36652\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 6\" width=\"148\" height=\"195\" \/><br \/>\nAnswer:<br \/>\ny = 4x\u00b2 + 11x &#8211; 3<br \/>\n4x\u00b2 + 11x &#8211; 3 = 0<br \/>\n4x\u00b2 + 12x &#8211; 1x &#8211; 3 = 0<br \/>\n4x(x + 3) &#8211; 1(x + 3) = 0<br \/>\n(x + 3)(4x &#8211; 1) = 0<br \/>\nx + 3 = 0 or 4x &#8211; 1 = 0<br \/>\nx = -3 or x = 1\/4<br \/>\nx = -3, 1\/4<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36653\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 7\" width=\"145\" height=\"182\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44316\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-31.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 31.1\" width=\"574\" height=\"536\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-31.1.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-31.1-300x280.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44317\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-31.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 31.2\" width=\"552\" height=\"335\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-31.2.png 552w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-31.2-300x182.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36654\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 8\" width=\"155\" height=\"192\" \/><br \/>\nAnswer:<br \/>\ny = -3x\u00b2 + 14x + 5<br \/>\n= -3x\u00b2 + 14x + 5 = 0<br \/>\n-3x\u00b2 + 15x &#8211; 1x + 5 = 0<br \/>\n-3x(x &#8211; 5) -1(x &#8211; 5) = 0<br \/>\n(x &#8211; 5)(-3x &#8211; 1) = 0<br \/>\nx = 5, x = -1\/3<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe area (in square feet) of the school sign can be represented by 15x<sup>2<\/sup> &#8211; x &#8211; 2.<br \/>\na. Write an expression that represents the length of the sign.<br \/>\nb. Describe two ways to find the area of the sign when x = 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36655\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 9\" width=\"271\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44318\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 33\" width=\"587\" height=\"373\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-33.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-33-300x191.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height h (in feet) above the water of a cliff diver is modeled by h = -16t<sup>2<\/sup> + 8t + 80, where t is the time (in seconds). How long is the diver in the air?<br \/>\nAnswer:<br \/>\nh = -16t<sup>2<\/sup> + 8t + 80<br \/>\n-16t<sup>2<\/sup> + 8t + 80 = 0<br \/>\nTake 8 as common.<br \/>\n8[-2t\u00b2 + t + 10] = 0<br \/>\n-2t\u00b2 + t + 10 = 0<br \/>\n-2t\u00b2 + 5t &#8211; 4t + 10 = 0<br \/>\n-2t\u00b2 &#8211; 4t + 5t + 10 = 0<br \/>\n-2t(t + 2) + 5(t + 2) = 0<br \/>\n(t + 2)(-2t + 5) = 0<br \/>\nt = -2 or t = 5\/2<br \/>\nSo, the t is 5\/2.<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe Parthenon in Athens, Greece, is an ancient structure that has a rectangular base. The length of the base of the Parthenon is 8 meters more than twice its width. The area of the base is about 2170 square meters. Find the length and width of the base.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44319\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 35.1\" width=\"574\" height=\"556\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-35.1.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-35.1-300x291.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44320\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 35.2\" width=\"575\" height=\"230\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-35.2.png 575w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-35.2-300x120.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe length of a rectangular birthday party invitation is 1 inch less than twice its width. The area of the invitation is 15 square inches. Will the invitation fi t in the envelope shown without being folded? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36656\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 10\" width=\"166\" height=\"110\" \/><br \/>\nAnswer:<br \/>\nArea = length \u00d7 width<br \/>\nw = x<br \/>\nl = 2x &#8211; 1<br \/>\nA = 15 sq. in<br \/>\nx(2x &#8211; 1) = 15<br \/>\n2x\u00b2 &#8211; x = 15<br \/>\n2x\u00b2 &#8211; x &#8211; 15 = 0<br \/>\n2x\u00b2 &#8211; 6x + 5x &#8211; 15 = 0<br \/>\n2x(x &#8211; 3) + 5(x &#8211; 3) = 0<br \/>\n(x &#8211; 3)(2x + 5) = 0<br \/>\nx = 3 or -5\/2<br \/>\nx = 3 or -2.5<br \/>\nx = 3<br \/>\nw = 3<br \/>\nl = 2x &#8211; 1<br \/>\nl = 2(3) &#8211; 1 = 5<\/p>\n<p>Question 37.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a binomial whose terms have a GCF of 3x.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44321\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 37\" width=\"470\" height=\"102\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-37.png 470w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-37-300x65.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nWithout factoring, determine which of the graphs represents the function g(x) = 21x<sup>2<\/sup> + 37x + 12 and which represents the function h(x) = 21x<sup>2<\/sup> &#8211; 37x + 12. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36657\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 11\" width=\"202\" height=\"189\" \/><br \/>\nAnswer:<br \/>\ng(x) = 21x<sup>2<\/sup> + 37x + 12<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195703 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Factoring-ax2-bx-c-7.6-Exercises_38.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Factoring ax2 + bx + c 7.6 Exercises_38\" width=\"315\" height=\"464\" \/><br \/>\nh(x) = 21x<sup>2<\/sup> &#8211; 37x + 12<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195704 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Factoring-ax2-bx-c-7.6-Exercises_38_2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Factoring ax2 + bx + c 7.6 Exercises_38_2\" width=\"380\" height=\"466\" \/><\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhen is it not possible to factor ax<sup>2<\/sup> + bx + c, where a \u2260 1? Give an example.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44322\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 39\" width=\"578\" height=\"88\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-39.png 578w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-39-300x46.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that to solve the equation 5x<sup>2<\/sup> + x &#8211; 4 = 2, you should start by factoring the left side as (5x &#8211; 4)(x + 1). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n5x<sup>2<\/sup> + x &#8211; 4 = 2<br \/>\n5x\u00b2 + x &#8211; 4 &#8211; 2 = 0<br \/>\n5x\u00b2 + x &#8211; 6 = 0<br \/>\n5x\u00b2 + 6x &#8211; 5x &#8211; 6 = 0<br \/>\n5x(x &#8211; 1) + 6(x &#8211; 1) = 0<br \/>\n(x &#8211; 1)(5x + 6) = 0<br \/>\nYour friend is not correct.<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nFor what values of t can 2x<sup>2<\/sup> + tx + 10 be written as the product of two binomials?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44323\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-41.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 41.1\" width=\"564\" height=\"617\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-41.1.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-41.1-274x300.png 274w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44324\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-41.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 41.2\" width=\"581\" height=\"66\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-41.2.png 581w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-41.2-300x34.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse algebra tiles to factor each polynomial modeled by the tiles. Show your work.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36658\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 12\" width=\"317\" height=\"125\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-12.png 317w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-12-300x118.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<br \/>\na. 2x\u00b2 + x +x + x + x + x &#8211; 1 &#8211; 1 &#8211; 1 = 2x\u00b2 + 5x &#8211; 3<br \/>\n=2x\u00b2 + 6x &#8211; 1x &#8211; 3<br \/>\n= 2x(x + 3) &#8211; 1(x + 1)<br \/>\n= (x + 3)(2x &#8211; 1)<\/p>\n<p>b. 3x\u00b2 &#8211; 2x &#8211; 1<br \/>\n3x\u00b2 &#8211; 3x + 1x &#8211; 1<br \/>\n3x(x &#8211; 1) + 1(x &#8211; 1)<br \/>\n(x &#8211; 1)(3x + 1)<\/p>\n<p>Question 43.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe length of a rectangle is 1 inch more than twice its width. The value of the area of the rectangle (in square inches) is 5 more than the value of the perimeter of the rectangle (in inches). Find the width.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44325\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 43.1\" width=\"586\" height=\"448\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.1.png 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.1-300x229.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44326\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 43.2\" width=\"587\" height=\"561\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.2.png 587w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.2-300x287.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44327\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 43.3\" width=\"568\" height=\"64\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.3.png 568w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-43.3-300x34.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA rectangular swimming pool is bordered by a concrete patio. The width of the patio is the same on every side. The area of the surface of the pool is equal to the area of the patio. What is the width of the patio?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36659\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-7-Polynomial-Equations-and-Factoring-7.6-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 7 Polynomial Equations and Factoring 7.6 13\" width=\"205\" height=\"153\" \/><br \/>\nAnswer:<br \/>\nl = 24 + 2x<br \/>\nw = 16 + 2x<br \/>\nA = (24 + 2x)(16 + 2x)<br \/>\n(24 + 2x)(16 + 2x) = 2(24)(16)<\/p>\n<p><strong>In Exercises 45\u201348, factor the polynomial.<\/strong><br \/>\nQuestion 45.<br \/>\n4k<sup>2<\/sup> + 7jk &#8211; 2j<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44328\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 45\" width=\"585\" height=\"527\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-45.png 585w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-45-300x270.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 46.<br \/>\n6x<sup>2<\/sup> + 5xy &#8211; 4y<sup>2<\/sup><br \/>\nAnswer:<br \/>\n6x\u00b2 + 5xy &#8211; 4y\u00b2<br \/>\n6x\u00b2 &#8211; 3xy + 8xy &#8211; 4y\u00b2<br \/>\n3x(2x &#8211; y) + 4y(2x &#8211; y)<br \/>\n(3x + 4y)(2x &#8211; y)<\/p>\n<p>Question 47.<br \/>\n-6a<sup>2<\/sup> + 19ab &#8211; 14b<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44329\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 47.1\" width=\"610\" height=\"611\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.1.png 610w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.1-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.1-150x150.png 150w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44330\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 47.2\" width=\"466\" height=\"37\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.2.png 466w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-47.2-300x24.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 48.<br \/>\n18m<sup>3<\/sup> + 39m<sup>2<\/sup>n &#8211; 15mn<sup>2<\/sup><br \/>\nAnswer:<br \/>\n18m<sup>3<\/sup> + 39m<sup>2<\/sup>n &#8211; 15mn\u00b2<br \/>\n3m(6m\u00b2 + 13mn &#8211; 5n\u00b2)<br \/>\n3m(6m\u00b2 + 10mn + 3mn &#8211; 5n\u00b2)<br \/>\n3m(3m(2m + n) &#8211; 5n(n + 2m))<br \/>\n3m(3m &#8211; 5n)(2m + n)<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Find the square root(s).<\/strong><br \/>\nQuestion 49.<br \/>\n\u00b1 \\(\\sqrt{64}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44331\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 49\" width=\"247\" height=\"33\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\sqrt{4}\\)<br \/>\nAnswer:<br \/>\n\\(\\sqrt{4}\\) = \u00b12<\/p>\n<p>Question 51.<br \/>\n&#8211; \\(\\sqrt{225}\\)<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44332\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 51\" width=\"277\" height=\"39\" \/><\/p>\n<p>Question 52.<br \/>\n\u00b1 \\(\\sqrt{81}\\)<br \/>\nAnswer: \u00b1 \\(\\sqrt{81}\\) = 9<\/p>\n<p><strong>Solve the system of linear equations by substitution. Check your solution.<\/strong><br \/>\nQuestion 53.<br \/>\ny = 3 + 7x<br \/>\ny &#8211; x = -3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44333\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-53.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 53.1\" width=\"402\" height=\"397\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-53.1.png 402w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-53.1-300x296.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44334\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-53.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 53.2\" width=\"497\" height=\"311\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-53.2.png 497w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-53.2-300x188.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Question 54.<br \/>\n2x = y + 2<br \/>\n-x + 3y = 14<br \/>\nAnswer:<br \/>\n2x = y + 2<br \/>\n-x + 3y = 14<br \/>\nx = 3y &#8211; 14<br \/>\n2(3y &#8211; 14) = y + 2<br \/>\n6y &#8211; 28 = y + 2<br \/>\n6y &#8211; y = 2 + 28<br \/>\n5y = 30<br \/>\ny = 30\/5<br \/>\ny = 6<br \/>\n2x = y + 2<br \/>\n2x = 6 + 2<br \/>\n2x = 8<br \/>\nx = 8\/2<br \/>\nx = 4<br \/>\nThe solution is x = 4 and y = 6.<\/p>\n<p>Question 55.<br \/>\n5x &#8211; 2y = 14<br \/>\n-7 = -2x + y<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44335\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-55.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 55.1\" width=\"389\" height=\"547\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-55.1.png 389w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-55.1-213x300.png 213w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44336\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-55.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.6 Question 55.2\" width=\"574\" height=\"190\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-55.2.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.6-Question-55.2-300x99.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 56.<br \/>\n-x &#8211; 8 = -y<br \/>\n9y &#8211; 12 + 3x = 0<br \/>\nAnswer:<br \/>\n-x &#8211; 8 = -y \u21d2 x + 8 = y<br \/>\n9y &#8211; 12 + 3x = 0<br \/>\n9(x + 8) &#8211; 12 + 3x = 0<br \/>\n9x + 72 &#8211; 12 + 3x = 0<br \/>\n12x + 60 = 0<br \/>\n12x = -60<br \/>\nx = -5<br \/>\nx + 8 = y<br \/>\n-5 + 8 = y<br \/>\ny = 3<\/p>\n<h3><a id=\"Lesson_7.7_Factoring_Special_Products\"><\/a>Lesson 7.7 Factoring Special Products<\/h3>\n<p><strong>Essential Question<\/strong> How can you recognize and factor special products?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Factoring Special ProductsWork with a partner. Use algebra tiles to write each polynomial as the product of two binomials. Check your answer by multiplying. State whether the product is a \u201cspecial product\u201d that you studied in Section 7.3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36660\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 1\" width=\"717\" height=\"526\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-1.png 717w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-1-300x220.png 300w\" sizes=\"(max-width: 717px) 100vw, 717px\" \/><\/p>\n<p>Answer:<br \/>\na. 4x\u00b2 &#8211; 1 = (2x)\u00b2 &#8211; (1)\u00b2<br \/>\n= (2x + 1)(2x &#8211; 1)<\/p>\n<p>b. 4x\u00b2 &#8211; 4x + 1<br \/>\n(a &#8211; b)\u00b2= a\u00b2 + b\u00b2 &#8211; 2ab<br \/>\n(2x &#8211; 1)\u00b2 = (2x)\u00b2 + (1)\u00b2 &#8211; 2(2x)(1)<br \/>\n= 4x\u00b2 + 1 &#8211; 4x<br \/>\nSo, 4x\u00b2 &#8211; 4x + 1 = (2x &#8211; 1)\u00b2<\/p>\n<p>c. 4x\u00b2 + 4x + 1<br \/>\n(a + b)\u00b2= a\u00b2 + b\u00b2 + 2ab<br \/>\n(2x &#8211; 1)\u00b2 = (2x)\u00b2 + (1)\u00b2 + 2(2x)(1)<br \/>\n= 4x\u00b2 + 1 + 4x<br \/>\nSo, 4x\u00b2 + 4x + 1 = (2x + 1)\u00b2<\/p>\n<p>d. 4x\u00b2 &#8211; 6x + 2<br \/>\n4x\u00b2 &#8211; 4x &#8211; 2x + 2<br \/>\n4x(x &#8211; 1) &#8211; 1(x &#8211; 1)<br \/>\n(x &#8211; 1)(4x &#8211; 1)<br \/>\n4x\u00b2 &#8211; 6x + 2 = (x &#8211; 1)(4x &#8211; 1)<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Factoring Special Products<br \/>\nWork with a partner. Use algebra tiles to complete the rectangular array at the left in three different ways, so that each way represents a different special product. Write each special product in standard form and in factored form.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36661\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 2\" width=\"225\" height=\"212\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you recognize and factor special products? Describe a strategy for recognizing which polynomials can be factored as special products.<br \/>\nAnswer: If there are only two terms then look for the sum of cubes or differences of squares or cubes. If there are three terms, look for squares of a difference or a sum. If there are three terms and the first coefficient is 1 then use simple trinomial factoring.<\/p>\n<p>Question 4.<br \/>\nUse the strategy you described in Question 3 to factor each polynomial.<br \/>\na. 25x<sup>2<\/sup> + 10x + 1<br \/>\nb. 25x<sup>2<\/sup> &#8211; 10x + 1<br \/>\nc. 25x<sup>2<\/sup> &#8211; 1<br \/>\nAnswer:<br \/>\na. 25x<sup>2<\/sup> + 10x + 1<br \/>\n25x\u00b2 + 5x + 5x + 1<br \/>\n= 5x(5x + 1) + 1(5x + 1)<br \/>\n= (5x + 1)(5x + 1)<br \/>\n= (5x + 1)\u00b2<\/p>\n<p>b. 25x<sup>2<\/sup> &#8211; 10x + 1<br \/>\n25x\u00b2 &#8211; 5x &#8211; 5x + 1<br \/>\n= 5x(5x &#8211; 1) -1(5x &#8211; 1)<br \/>\n= (5x &#8211; 1)(5x &#8211; 1)<br \/>\n= (5x &#8211; 1)\u00b2<\/p>\n<p>c. 25x<sup>2<\/sup> &#8211; 1<br \/>\n25x\u00b2 &#8211; 1<br \/>\n(5x &#8211; 1)(5x + 1)<br \/>\n= (5x)\u00b2 &#8211; 1\u00b2<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; 36<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> &#8211; 36<br \/>\nx\u00b2 &#8211; 36 can be written as x\u00b2 &#8211; 6\u00b2<br \/>\nx\u00b2 &#8211; 6\u00b2 = (x + 6)(x &#8211; 6)<\/p>\n<p>Question 2.<br \/>\n100 &#8211; m<sup>2<\/sup><br \/>\nAnswer:<br \/>\n100 &#8211; m\u00b2<br \/>\n10\u00b2 &#8211; m\u00b2 = (10 + m)(10 &#8211; m)<\/p>\n<p>Question 3.<br \/>\n9n<sup>2<\/sup> &#8211; 16<br \/>\nAnswer:<br \/>\n9n\u00b2 &#8211; 16<br \/>\n(3n)\u00b2 &#8211; 4\u00b2 = (3n + 4)(3n &#8211; 4)<\/p>\n<p>Question 4.<br \/>\n16h<sup>2<\/sup> &#8211; 49<br \/>\nAnswer:<br \/>\n16h\u00b2 &#8211; 49<br \/>\n16h\u00b2 &#8211; 49 = (4h)\u00b2 &#8211; 7\u00b2 = (4h + 7)(4h &#8211; 7)<\/p>\n<p><strong>Use a special product pattern to evaluate the expression.<\/strong><br \/>\nQuestion 5.<br \/>\n36<sup>2<\/sup> &#8211; 34<sup>2<\/sup><br \/>\nAnswer:<br \/>\n36\u00b2 &#8211; 34\u00b2<br \/>\n= (36 \u00d7 36) &#8211; (34 \u00d7 34)<br \/>\n= 1296 &#8211; 1156<br \/>\n= 140<\/p>\n<p>Question 6.<br \/>\n47<sup>2<\/sup> &#8211; 44<sup>2<\/sup><br \/>\nAnswer:<br \/>\n47\u00b2 &#8211; 44\u00b2<br \/>\n= (47 \u00d7 47) &#8211; (44 \u00d7 44)<br \/>\n= 2209 &#8211; 1936<br \/>\n= 273<\/p>\n<p>Question 7.<br \/>\n55<sup>2<\/sup> &#8211; 50<sup>2<\/sup><br \/>\nAnswer:<br \/>\n55\u00b2 &#8211; 50\u00b2<br \/>\n= (55 \u00d7 55) &#8211;\u00a0 (50 \u00d7 50)<br \/>\n= 3025 &#8211; 2500<br \/>\n= 525<\/p>\n<p>Question 8.<br \/>\n28<sup>2<\/sup> &#8211; 24<sup>2<\/sup><br \/>\nAnswer:<br \/>\n28\u00b2 &#8211; 24\u00b2<br \/>\n= (28 \u00d7 28) &#8211; (24 \u00d7 24)<br \/>\n= 784 &#8211; 576<br \/>\n= 208<\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 9.<br \/>\nm<sup>2<\/sup> &#8211; 2m + 1<br \/>\nAnswer:<br \/>\nm\u00b2 &#8211; 2m + 1<br \/>\n1 \u00d7 1 = 1<br \/>\n= m\u00b2 &#8211; 1m &#8211; 1m + 1<br \/>\n= m(m &#8211; 1) &#8211; 1(m &#8211; 1)<br \/>\n= (m &#8211; 1)(m &#8211; 1)<\/p>\n<p>Question 10.<br \/>\nd<sup>2<\/sup> &#8211; 10d + 25<br \/>\nAnswer:<br \/>\nd\u00b2 &#8211; 10d + 25<br \/>\n5 \u00d7 5 = 25<br \/>\n5 + 5 = 10<br \/>\nd\u00b2 &#8211; 5d &#8211; 5d + 25<br \/>\nd(d &#8211; 5) &#8211; 5(d &#8211; 5)<br \/>\n(d &#8211; 5)(d &#8211; 5)<\/p>\n<p>Question 11.<br \/>\n9z<sup>2<\/sup> + 36z + 36<br \/>\nAnswer:<br \/>\n9z\u00b2 + 36z + 36<br \/>\n9z\u00b2 + 18z + 18z + 36<br \/>\n9z(z + 2) + 18(z + 2)<br \/>\n(z + 2)(9z + 18)<\/p>\n<p>Solve the equation.<br \/>\nQuestion 12.<br \/>\na<sup>2<\/sup> + 6a + 9 = 0<br \/>\nAnswer:<br \/>\na\u00b2 + 6a + 9 = 0<br \/>\n9 \u00d7 1 = 9<br \/>\n3 \u00d7 3 = 9<br \/>\n3 + 3 = 6<br \/>\na\u00b2 + 3a + 3a + 9 = 0<br \/>\na(a + 3) + 3(a + 3) = 0<br \/>\n(a + 3)(a + 3) = 0<br \/>\na + 3 = 0 or a + 3 = 0<br \/>\na = -3, -3<\/p>\n<p>Question 13.<br \/>\nw<sup>2<\/sup> &#8211; \\(\\frac{7}{3}\\)w + \\(\\frac{49}{36}\\) = 0<br \/>\nAnswer:<br \/>\nw\u00b2 &#8211; \\(\\frac{7}{3}\\)w + \\(\\frac{49}{36}\\) = 0<br \/>\nw\u00b2 &#8211; 2. \\(\\frac{7}{6}\\)w + (\\(\\frac{7}{6}\\))\u00b2 = 0<br \/>\n(w &#8211; \\(\\frac{7}{6}\\))\u00b2 = 0<br \/>\nw &#8211; \\(\\frac{7}{6}\\) = 0<br \/>\nw = \\(\\frac{7}{6}\\)<\/p>\n<p>Question 14.<br \/>\nn<sup>2<\/sup> &#8211; 81 = 0<br \/>\nAnswer:<br \/>\nn<sup>2<\/sup> &#8211; 81 = 0<br \/>\nn\u00b2 &#8211; 9\u00b2 = 0<br \/>\n(n + 9)(n &#8211; 9) = 0<br \/>\nn = -9, 9<\/p>\n<p>Question 15.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe golf ball does not hit the pine tree. After how many seconds does the ball hit the ground?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Factoring_Special_Products_7.7_Exercises\"><\/a>Factoring Special Products 7.7 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>REASONING<\/strong><br \/>\nCan you use the perfect square trinomial pattern to factor y<sup>2<\/sup> + 16y + 64? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44337\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 1\" width=\"577\" height=\"85\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-1.png 577w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-1-300x44.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich polynomial does not belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36662\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 3\" width=\"487\" height=\"43\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-3.png 487w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-3-300x26.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nAnswer: k\u00b2 + 25 does not belong with the other three.<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, factor the polynomial.<\/strong><br \/>\nQuestion 3.<br \/>\nm<sup>2<\/sup> &#8211; 49<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44338\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 3\" width=\"310\" height=\"97\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-3.png 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-3-300x94.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 4.<br \/>\nz<sup>2<\/sup> &#8211; 81<br \/>\nAnswer:<br \/>\nz\u00b2 &#8211; 81 = z\u00b2 &#8211; 9\u00b2<br \/>\n= (z + 9)(z &#8211; 9)<\/p>\n<p>Question 5.<br \/>\n64 &#8211; 81d<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44339\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 5\" width=\"341\" height=\"99\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-5.png 341w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-5-300x87.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 6.<br \/>\n25 &#8211; 4x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n25 &#8211; 4x\u00b2<br \/>\n= 5\u00b2 &#8211; (2x)\u00b2<br \/>\n= (5 + 2x)(5 &#8211; 2x)<\/p>\n<p>Question 7.<br \/>\n225a<sup>2<\/sup> &#8211; 36b<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44340\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 7\" width=\"398\" height=\"138\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-7.png 398w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-7-300x104.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 8.<br \/>\n16x<sup>2<\/sup> &#8211; 169y<sup>2<\/sup><br \/>\nAnswer:<br \/>\n16x\u00b2 &#8211; 169y\u00b2<br \/>\n= (4x)\u00b2 &#8211; (13y)\u00b2<br \/>\n= (4x + 13y)(4x &#8211; 13y)<\/p>\n<p><strong>In Exercises 9\u201314, use a special product pattern to evaluate the expression.<\/strong><br \/>\nQuestion 9.<br \/>\n12<sup>2<\/sup> &#8211; 9<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44341\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 9\" width=\"293\" height=\"134\" \/><\/p>\n<p>Question 10.<br \/>\n19<sup>2<\/sup> &#8211; 11<sup>2<\/sup><br \/>\nAnswer:<br \/>\n19\u00b2 &#8211; 11\u00b2<br \/>\n= (19 + 11)(19 &#8211; 11)<br \/>\n= 30 \u00d7 8<br \/>\n= 240<\/p>\n<p>Question 11.<br \/>\n78<sup>2<\/sup> &#8211; 72<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44342\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 11\" width=\"313\" height=\"134\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-11.png 313w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-11-300x128.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<p>Question 12.<br \/>\n54<sup>2<\/sup> &#8211; 52<sup>2<\/sup><br \/>\nAnswer:<br \/>\n54\u00b2 &#8211; 52\u00b2<br \/>\n= (54 + 52)(54 &#8211; 52)<br \/>\n= (106)(2)<br \/>\n= 212<\/p>\n<p>Question 13.<br \/>\n53<sup>2<\/sup> &#8211; 47<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44343\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 13\" width=\"323\" height=\"136\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-13.png 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-13-300x126.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 14.<br \/>\n39<sup>2<\/sup> &#8211; 36<sup>2<\/sup><br \/>\nAnswer:<br \/>\n39\u00b2 &#8211; 36\u00b2<br \/>\n= (39 + 36)(39 &#8211; 36)<br \/>\n= (75)(3)<br \/>\n= 225<\/p>\n<p><strong>In Exercises 15\u201322, factor the polynomial.<\/strong><br \/>\nQuestion 15.<br \/>\nh<sup>2<\/sup> + 12h + 36<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44344\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 15\" width=\"358\" height=\"105\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-15.png 358w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-15-300x88.png 300w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/p>\n<p>Question 16.<br \/>\np<sup>2<\/sup> + 30p + 225<br \/>\nAnswer:<br \/>\np\u00b2 + 30p + 225<br \/>\np\u00b2 + 2(15)(p) + 15\u00b2<br \/>\n(p + 15)\u00b2<\/p>\n<p>Question 17.<br \/>\ny<sup>2<\/sup> &#8211; 22y + 121<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44345\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 17\" width=\"383\" height=\"106\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-17.png 383w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-17-300x83.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n<p>Question 18.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 4<br \/>\nAnswer:<br \/>\nx\u00b2 &#8211; 4x + 4<br \/>\n= x\u00b2 &#8211; 2(2)x + 2\u00b2<br \/>\n= (x &#8211; 2)\u00b2<\/p>\n<p>Question 19.<br \/>\na<sup>2<\/sup> &#8211; 28a + 196<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44346\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 19\" width=\"377\" height=\"100\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-19.png 377w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-19-300x80.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/p>\n<p>Question 20.<br \/>\nm<sup>2<\/sup> + 24m + 144<br \/>\nAnswer:<br \/>\nm\u00b2 + 24m + 144<br \/>\n= m\u00b2 + 2(12)m + 12\u00b2<br \/>\n= (m + 12)\u00b2<\/p>\n<p>Question 21.<br \/>\n25n<sup>2<\/sup> + 20n + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44347\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 21\" width=\"392\" height=\"101\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-21.png 392w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-21-300x77.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 22.<br \/>\n49a<sup>2<\/sup> &#8211; 14a + 1<br \/>\nAnswer:<br \/>\n49a\u00b2 &#8211; 14a + 1<br \/>\n= (7a)\u00b2 &#8211; 2(7)(a) + 1<br \/>\n= (7a &#8211; 1)\u00b2<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 23 and 24, describe and correct the error in factoring the polynomial.<br \/>\nQuestion 23.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36663\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 4\" width=\"317\" height=\"71\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-4.png 317w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-4-300x67.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44348\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 23\" width=\"582\" height=\"161\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-23.png 582w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-23-300x83.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36664\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 5\" width=\"316\" height=\"71\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-5.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-5-300x67.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\ny\u00b2 &#8211; 6y + 9<br \/>\n= y\u00b2 &#8211; 2(3)(y) + 3\u00b2<br \/>\n= (y &#8211; 3)\u00b2<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe area (in square centimeters) of a square coaster can be represented by d<sup>2<\/sup> + 8d + 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36665\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 6\" width=\"133\" height=\"172\" \/><br \/>\na. Write an expression that represents the side length of the coaster.<br \/>\nb. Write an expression for the perimeter of the coaster.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44349\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 25\" width=\"551\" height=\"334\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-25.png 551w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-25-300x182.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe polynomial represents the area (in square feet) of the square playground.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36666\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 7\" width=\"174\" height=\"163\" \/><br \/>\na. Write a polynomial that represents the side length of the playground.<br \/>\nb. Write an expression for the perimeter of the playground.<br \/>\nAnswer:<br \/>\nA = x\u00b2 &#8211; 30x + 225<br \/>\nA = x\u00b2 &#8211; 2(15)x + 15\u00b2<br \/>\nA = (x &#8211; 15)\u00b2<br \/>\ns = x &#8211; 15<br \/>\nP = 4 \u00d7 side<br \/>\nP = 4 \u00d7 (x &#8211; 15)<br \/>\nP = 4x &#8211; 60<\/p>\n<p><strong>In Exercises 27\u201334, solve the equation.<\/strong><br \/>\nQuestion 27.<br \/>\nz<sup>2<\/sup> &#8211; 4 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44350\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 27\" width=\"469\" height=\"254\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-27.png 469w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-27-300x162.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Question 28.<br \/>\n4x<sup>2<\/sup> = 49<br \/>\nAnswer:<br \/>\n4x\u00b2 = 49<br \/>\n4x\u00b2 &#8211; 49 = 0<br \/>\n(2x)\u00b2 &#8211; 7\u00b2 = 0<br \/>\n(2x + 7)(2x &#8211; 7) = 0<br \/>\n2x + 7 = 0 or 2x &#8211; 7 = 0<br \/>\nx = -7\/2 or x = 7\/2<br \/>\nx = -7\/2, 7\/2<\/p>\n<p>Question 29.<br \/>\nk<sup>2<\/sup> &#8211; 16k + 64 = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44351\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 29\" width=\"396\" height=\"245\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-29.png 396w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-29-300x186.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p>Question 30.<br \/>\ns<sup>2<\/sup> + 20s + 100 = 0<br \/>\nAnswer:<br \/>\ns\u00b2 + 20s + 100 = 0<br \/>\ns\u00b2 + 2(10)(s) + 10\u00b2 = 0<br \/>\n(s + 10)\u00b2 = 0<br \/>\ns + 10 = 0<br \/>\ns = -10<\/p>\n<p>Question 31.<br \/>\nn<sup>2<\/sup> + 9 = 6n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44352\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 31\" width=\"398\" height=\"308\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-31.png 398w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-31-300x232.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 32.<br \/>\ny<sup>2<\/sup> = 12y &#8211; 36<br \/>\nAnswer:<br \/>\ny\u00b2 = 12y &#8211; 36<br \/>\ny\u00b2 &#8211; 12y + 36 = 0<br \/>\ny\u00b2 &#8211; 2(6)y + 6\u00b2 = 0<br \/>\n(y &#8211; 6)\u00b2 = 0<br \/>\ny &#8211; 6 = 0<br \/>\ny = 6<\/p>\n<p>Question 33.<br \/>\ny<sup>2<\/sup> + \\(\\frac{1}{2}\\)y = &#8211; 1 \u2014 16<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44353\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 33\" width=\"439\" height=\"625\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-33.png 439w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-33-211x300.png 211w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Question 34.<br \/>\n&#8211; \\(\\frac{4}{3}\\)x + \\(\\frac{4}{9}\\) = -x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n&#8211; \\(\\frac{4}{3}\\)x + \\(\\frac{4}{9}\\) = -x<sup>2<\/sup><br \/>\nx\u00b2 &#8211; \\(\\frac{4}{3}\\)x + \\(\\frac{4}{9}\\) = 0<br \/>\nx\u00b2 &#8211; 2(\\(\\frac{2}{3}\\))x + \\(\\frac{2}{3}\\)\u00b2 = 0<br \/>\n(x &#8211; \\(\\frac{2}{3}\\))\u00b2 = 0<br \/>\nx &#8211; \\(\\frac{2}{3}\\) = 0<br \/>\nx = \\(\\frac{2}{3}\\)<\/p>\n<p><strong>In Exercises 35\u201340, factor the polynomial.<\/strong><br \/>\nQuestion 35.<br \/>\n3z<sup>2<\/sup> &#8211; 27<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44354\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 35\" width=\"310\" height=\"141\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-35.png 310w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-35-300x136.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 36.<br \/>\n2m<sup>2<\/sup> &#8211; 50<br \/>\nAnswer:<br \/>\n2m<sup>2<\/sup> &#8211; 50 = 2(m\u00b2 &#8211; 25)<br \/>\n= 2(m + 5)(m &#8211; 5)<br \/>\nSo, 2m<sup>2<\/sup> &#8211; 50 = 2(m + 5)(m &#8211; 5)<\/p>\n<p>Question 37.<br \/>\n4y<sup>2<\/sup> &#8211; 16y + 16<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44355\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 37\" width=\"387\" height=\"139\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-37.png 387w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-37-300x108.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 38.<br \/>\n8k<sup>2<\/sup> + 80k + 200<br \/>\nAnswer:<br \/>\n8k<sup>2<\/sup> + 80k + 200 = 8(k\u00b2 + 10k + 25)<br \/>\n= 8(k\u00b2 + 5k + 5k + 25)<br \/>\n= 8(k(k + 5) + 5(k + 5))<br \/>\n= 8(k + 5)(k + 5)<\/p>\n<p>Question 39.<br \/>\n50y<sup>2<\/sup> + 120y + 72<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44356\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 39\" width=\"443\" height=\"135\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-39.png 443w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-39-300x91.png 300w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Question 40.<br \/>\n27m<sup>2<\/sup> &#8211; 36m + 12<br \/>\nAnswer:<br \/>\n27m<sup>2<\/sup> &#8211; 36m + 12 = 3[9m\u00b2 &#8211; 12m + 4]<br \/>\n= 3[9m\u00b2 &#8211; 6m &#8211; 6m + 4]<br \/>\n= 3[3m(3m &#8211; 2) &#8211; 2(3m &#8211; 2)]<br \/>\n= 3[(3m &#8211; 2)(3m &#8211; 2)]<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nWhile standing on a ladder, you drop a paintbrush. The function represents the height y (in feet) of the paintbrush t seconds after it is dropped. After how many seconds does the paintbrush land on the ground?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36667\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 8\" width=\"151\" height=\"168\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44357\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 41\" width=\"567\" height=\"411\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-41.png 567w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-41-300x217.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function represents the height y (in feet) of a grasshopper jumping straight up from the ground t seconds after the start of the jump. After how many seconds is the grasshopper 1 foot off the ground?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36668\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 9\" width=\"126\" height=\"184\" \/><br \/>\nAnswer:<br \/>\ny = 1 foot<br \/>\ny = &#8211; 16t\u00b2 + 8t<br \/>\n-16t\u00b2 + 8t = 1<br \/>\n-16t\u00b2 + 8t &#8211; 1 = 0<br \/>\n16t\u00b2 &#8211; 8t + 1 = 0<br \/>\n(4t)\u00b2 &#8211; 2(4t)(1) + 1\u00b2 = 0<br \/>\n(4t &#8211; 1)\u00b2 = 0<br \/>\n4t &#8211; 1 = 0<br \/>\n4t = 1<br \/>\nt = 1\/4<br \/>\nt = 0.25 seconds<\/p>\n<p>Question 43.<br \/>\n<strong>REASONING<\/strong><br \/>\nTell whether the polynomial can be factored. If not, change the constant term so that the polynomial is a perfect square trinomial.<br \/>\na. w<sup>2<\/sup> + 18w + 84<br \/>\nb. y<sup>2<\/sup> &#8211; 10y + 23<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44358\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-43.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 43.1\" width=\"574\" height=\"395\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-43.1.png 574w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-43.1-300x206.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44359\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-43.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 43.2\" width=\"584\" height=\"404\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-43.2.png 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-43.2-300x208.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse algebra tiles to factor each polynomial modeled by the tiles. Show your work.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36669\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 10\" width=\"327\" height=\"123\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-10.png 327w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-10-300x113.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\na. 4x\u00b2 &#8211; 1<br \/>\n= (2x)\u00b2 &#8211; 1\u00b2<br \/>\n= (2x &#8211; 1)(2x + 1)<\/p>\n<p>b. 4x\u00b2 &#8211; 4x + 1<br \/>\n= 4x\u00b2 &#8211; 2(2)(x) + 1\u00b2<br \/>\n= (2x)\u00b2 &#8211; 2(2)x + 1\u00b2<br \/>\n= (2x &#8211; 1)\u00b2<\/p>\n<p>Question 45.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nDescribe two methods you can use to simplify (2x &#8211; 5)<sup>2<\/sup> &#8211; (x &#8211; 4)<sup>2<\/sup>. Which one would you use? Explain.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44360\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 45\" width=\"541\" height=\"171\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-45.png 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-45-300x95.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe figure shows a large square with an area of a<sup>2<\/sup> that contains a smaller square with an area of b<sup>2<\/sup>.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36670\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 11\" width=\"201\" height=\"167\" \/><br \/>\na. Describe the regions that represent a<sup>2<\/sup> &#8211; b<sup>2<\/sup>. How can you rearrange these regions to show that a<sup>2<\/sup> &#8211; b<sup>2<\/sup> = (a + b)(a &#8211; b)?<br \/>\nb. How can you use the figure to show that (a &#8211; b)<sup>2<\/sup> = a<sup>2<\/sup> &#8211; 2ab + b<sup>2<\/sup>?<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou hang nine identical square picture frames on a wall.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36671\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 12\" width=\"171\" height=\"168\" \/><br \/>\na. Write a polynomial that represents the area of the picture frames, not including the pictures.<br \/>\nb. The area in part (a) is 81 square inches. What is the side length of one of the picture frames? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44361\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 47.1\" width=\"584\" height=\"567\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-47.1.png 584w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-47.1-300x291.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44362\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 47.2\" width=\"501\" height=\"224\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-47.2.png 501w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-47.2-300x134.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe composite solid is made up of a cube and a rectangular prism.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36672\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 13\" width=\"172\" height=\"99\" \/><br \/>\na. Write a polynomial that represents the volume of the composite solid.<br \/>\nAnswer:<br \/>\nV = lbh<br \/>\nV = x \u00d7 x \u00d7 x<br \/>\nV = x\u00b3<br \/>\nV = 4 \u00d7 4 \u00d7 x<br \/>\nV = 16x<br \/>\nV = x\u00b3 + 16x<\/p>\n<p>b. The volume of the composite solid is equal to 25x. What is the value of x? Explain your reasoning.<br \/>\nAnswer:<br \/>\nV = x\u00b3 + 16x<br \/>\nx\u00b3 + 16x = 25x<br \/>\nx\u00b3 + 16x &#8211; 25x = 0<br \/>\nx\u00b3 &#8211; 9x = 0<br \/>\nx(x\u00b2 &#8211; 9) = 0<br \/>\nx(x\u00b2 &#8211; 3\u00b2) = 0<br \/>\nx(x + 3)(x &#8211; 3)<br \/>\nx = 0 or x + 3 = 0 or x &#8211; 3 = 0<br \/>\nx = 0, -3, 3<br \/>\nx = 3 in.<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write the prime factorization of the number.<\/strong><br \/>\nQuestion 49.<br \/>\n50<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44363\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 49\" width=\"480\" height=\"142\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-49.png 480w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-49-300x89.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>Question 50.<br \/>\n44<br \/>\nAnswer:<br \/>\n44 = 2 \u00d7 2 \u00d7 11<br \/>\nThe prime factorization of 44 are 2 \u00d7 2 \u00d7 11<\/p>\n<p>Question 51.<br \/>\n85<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44364\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 51\" width=\"368\" height=\"102\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-51.png 368w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-51-300x83.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/p>\n<p>Question 52.<br \/>\n96<br \/>\nAnswer:<br \/>\n96 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3<br \/>\nThe prime factorization of 96 are 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3<\/p>\n<p><strong>Graph the inequality in a coordinate plane.<\/strong><br \/>\nQuestion 53.<br \/>\ny \u2264 4x &#8211; 1<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44365\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 53\" width=\"586\" height=\"325\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-53.png 586w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-53-300x166.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 54.<br \/>\ny &gt; &#8211; \\(\\frac{1}{2}\\)x + 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195479 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Exercises_54.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.7 Exercises_54\" width=\"628\" height=\"547\" \/><\/p>\n<p>Question 55.<br \/>\n4y &#8211; 12 \u2265 8x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44366\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.7 Question 55\" width=\"591\" height=\"522\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-55.png 591w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Question-55-300x265.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 56.<br \/>\n3y + 3 &lt; x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-195478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-7.7-Exercises_56-300x297.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring 7.7 Exercises_56\" width=\"300\" height=\"297\" \/><\/p>\n<h3><a id=\"Lesson_7.8_Factoring_Polynomials_Completely\"><\/a>Lesson 7.8 Factoring Polynomials Completely<\/h3>\n<p><strong>Essential Question<\/strong> How can you factor a polynomial completely?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing a Product of Linear Factors<br \/>\nWork with a partner. Write the product represented by the algebra tiles. Then multiply to write the polynomial in standard form.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36673\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 1\" width=\"378\" height=\"228\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-1.png 378w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-1-300x181.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nAnswer:<br \/>\na. (x + 1)(x + 1)(-2) = (x + 1)\u00b2 &#8211; 2 = x\u00b2 + 2x + 1 &#8211; 2 = x\u00b2 + 2x &#8211; 1<br \/>\nb. (x + 2)(x + 1)(-x) = (x + 2)(-x\u00b2 &#8211; x) = -x\u00b3 &#8211; 2x\u00b2 &#8211; x\u00b2 &#8211; 2x = -x\u00b2 &#8211; 3x\u00b2 &#8211; 2x<br \/>\nc. (x + 3)(x)(2) = (x\u00b2 + 3x)2 = 2x\u00b2 + 6x<br \/>\nd. (x + 1)(x &#8211; 1)(x) = (x\u00b2 &#8211; 1)x = x\u00b3 &#8211; x<br \/>\ne. (-x + 1)(x + 1)(-x) = (1 &#8211; x\u00b2)(-x) = -x + x\u00b3<br \/>\nf. (-x &#8211; 1)(x + 1)(-2) = (-x\u00b2 &#8211; 1)(-2) = 2x\u00b2 + 2<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Matching Standard and Factored Forms<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36674\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 2\" width=\"222\" height=\"163\" \/><br \/>\nWork with a partner. Match the standard form of the polynomial with the equivalent factored form. Explain your strategy.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36675\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 3\" width=\"396\" height=\"396\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-3.png 396w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-3-300x300.png 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-3-150x150.png 150w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><br \/>\nAnswer:<br \/>\na. x\u00b3 + x\u00b2 = x\u00b2(x + 1) &#8211; <strong>J<\/strong><br \/>\nb. x\u00b3 &#8211; x = x(x\u00b2 &#8211; 1) = x(x + 1)(x &#8211; 1) &#8211; <strong>A<br \/>\n<\/strong>c. x\u00b3 + x\u00b2 &#8211; 2x = x(x\u00b2 + x &#8211; 2) = x(x\u00b2 + 2x &#8211; 1x &#8211; 2) = x(x(x + 2) &#8211; 1(x + 2)) = x(x &#8211; 1)(x + 2) &#8211;<strong> D<br \/>\n<\/strong>d. x\u00b3 &#8211; 4x\u00b2 + 4x = x(x\u00b2 &#8211; 4x + 4) = x(x &#8211; 2)\u00b2 &#8211; <strong>G<\/strong><br \/>\ne. x\u00b3 &#8211; 2x\u00b2 &#8211; 3x = x(x\u00b2 &#8211; 2x &#8211; 3) = x(x\u00b2 &#8211; 3x + 1x &#8211; 3) = x(x(x &#8211; 3) + 1(x &#8211; 3)) = x(x &#8211; 3)(x + 1) &#8211; <strong>N<\/strong><br \/>\nf. x\u00b3 &#8211; 2x\u00b2 + x = x(x\u00b2 &#8211; 2x + 1) = x(x &#8211; 1)\u00b2 &#8211; <strong>B<\/strong><br \/>\ng. x\u00b3 &#8211; 4x = x(x\u00b2 &#8211; 4) = x(x + 2)(x &#8211; 2) &#8211; <strong>F<\/strong><br \/>\nh. x\u00b3 + 2x\u00b2 = x\u00b2(x + 2) &#8211; <strong>L<\/strong><br \/>\ni. x\u00b3 &#8211; x\u00b2 = x\u00b2(x &#8211; 1) &#8211; <strong>I<\/strong><br \/>\nj. x\u00b3 &#8211; 3x\u00b2 + 2x = x(x\u00b2 &#8211; 3x + 2) = x(x\u00b2 &#8211; 2x &#8211; 1x + 2) = x(x(x &#8211; 2) &#8211;\u00a0 1(x &#8211; 2)) = x(x &#8211; 2)(x &#8211; 1) &#8211; <strong>E<\/strong><br \/>\nk. x\u00b3 + 2x\u00b2 &#8211; 3x = x(x\u00b2 + 2x &#8211; 3) = x(x\u00b2 + 3x &#8211; 1x &#8211; 3) = x(x(x + 3) &#8211; 1(x + 3)) = x(x + 3)(x &#8211; 1) &#8211; <strong>M<\/strong><br \/>\ni. x\u00b3 &#8211; 4x\u00b2 + 3x = x(x\u00b2 &#8211; 4x + 3) = x(x\u00b2 &#8211; 3x &#8211; 1x + 3) = x(x(x &#8211; 3) &#8211; 1(x &#8211; 3)) = x(x &#8211; 3)(x &#8211; 1) &#8211; <strong>O<\/strong><br \/>\nm. x\u00b3 &#8211; 2x\u00b2 = x\u00b2(x &#8211; 2) &#8211; <strong>K<\/strong><br \/>\nn. x\u00b3 + 4x\u00b2 + 4x = x(x\u00b2 + 4x + 4) = x(x + 2)\u00b2 &#8211; <strong>H<\/strong><br \/>\no. x\u00b3 + 2x\u00b2 + x = x(x\u00b2 + 2x + 1) = x(x + 1)\u00b2 &#8211; <strong>C<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-196115 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-3.png\" alt=\"Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-3\" width=\"396\" height=\"396\" \/><\/strong><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you factor a polynomial completely?<br \/>\nAnswer: Group the first two terms together and then the last terms together. Factor out a GCF from each separate binomial. Factor out the common binomial.<\/p>\n<p>Question 4.<br \/>\nUse your answer to Question 3 to factor each polynomial completely.<br \/>\na. x<sup>3<\/sup> + 4x<sup>2<\/sup> + 3x<br \/>\nb. x<sup>3<\/sup> &#8211; 6x<sup>2<\/sup> + 9x<br \/>\nc. x<sup>3<\/sup> + 6x<sup>2<\/sup> + 9x<br \/>\nAnswer:<br \/>\na. x<sup>3<\/sup> + 4x<sup>2<\/sup> + 3x = x(x\u00b2 + 4x + 3) = x(x\u00b2 + 3x + 1x + 3) = x(x(x + 3) + 1(x + 3)) = x(x + 1)(x + 3)<br \/>\nb. x<sup>3<\/sup> &#8211; 6x<sup>2<\/sup> + 9x = x(x\u00b2 &#8211; 6x + 9) = x(x &#8211; 3)\u00b2<br \/>\nc. x<sup>3<\/sup> + 6x<sup>2<\/sup> + 9x= x(x\u00b2 + 6x + 9) = x(x + 3)\u00b2<\/p>\n<p><strong>Factor the polynomial by grouping.<\/strong><br \/>\nQuestion 1.<br \/>\na<sup>3<\/sup> + 3a<sup>2<\/sup> + a + 3<br \/>\nAnswer:<br \/>\na<sup>3<\/sup> + 3a<sup>2<\/sup> + a + 3<br \/>\na\u00b3 + 3a\u00b2 + (a + 3)<br \/>\na\u00b2(a + 3) + 1(a + 3)<br \/>\n(a\u00b2 + 1)(a + 3)<\/p>\n<p>Question 2.<br \/>\ny<sup>2<\/sup> + 2x + yx + 2y<br \/>\nAnswer:<br \/>\ny\u00b2 + 2x + xy + 2y<br \/>\ny(y + x) + 2(x + y)<br \/>\n(y + 2)(x + y)<\/p>\n<p><strong>Factor the polynomial completely.<\/strong><br \/>\nQuestion 3.<br \/>\n3x<sup>3<\/sup> &#8211; 12x<br \/>\nAnswer:<br \/>\n3x\u00b3 &#8211; 12x<br \/>\n3x(x\u00b2 &#8211; 4)<\/p>\n<p>Question 4.<br \/>\n2y<sup>3<\/sup> &#8211; 12y<sup>2<\/sup> + 18y<br \/>\nAnswer:<br \/>\n2y\u00b3 &#8211; 12y\u00b2 + 18y<br \/>\n2y(y\u00b2 &#8211; 6y + 9)<br \/>\n2y(y &#8211; 3)\u00b2<\/p>\n<p>Question 5.<br \/>\nm<sup>3<\/sup> &#8211; 2m<sup>2<\/sup> &#8211; 8m<br \/>\nAnswer:<br \/>\nm\u00b3 &#8211; 2m\u00b2 &#8211; 8m<br \/>\nm(m\u00b2 &#8211; 2m &#8211; 8)<br \/>\nm(m\u00b2 &#8211; 4m + 2m &#8211; 8)<br \/>\nm(m(m &#8211; 4) + 2(m &#8211; 4))<br \/>\nm(m &#8211; 4)(m + 2)<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 6.<br \/>\nw<sup>3<\/sup> &#8211; 8w<sup>2<\/sup> + 16w = 0<br \/>\nAnswer:<br \/>\nw\u00b3 &#8211; 8w\u00b2 + 16w = 0<br \/>\nw(w\u00b2 &#8211; 8w + 16) = 0<br \/>\nw\u00b2 &#8211; 8w + 16 = 0<br \/>\nw\u00b2 &#8211; 4w &#8211; 4w + 16 = 0<br \/>\nw(w &#8211; 4) -4 (w &#8211; 4) = 0<br \/>\n(w &#8211; 4)(w &#8211; 4) = 0<br \/>\nw = 4, 4<\/p>\n<p>Question 7.<br \/>\nx<sup>3<\/sup> &#8211; 25x = 0<br \/>\nAnswer:<br \/>\nx\u00b3 &#8211; 25x = 0<br \/>\nx(x\u00b2 &#8211; 25) = 0<br \/>\nx\u00b2 &#8211; 25 = 0<br \/>\nx\u00b2 &#8211; 5\u00b2 = 0<br \/>\nx\u00b2 = 5\u00b2<br \/>\nx = 5<\/p>\n<p>Question 8.<br \/>\nc<sup>3<\/sup> &#8211; 7c<sup>2<\/sup> + 12c = 0<br \/>\nAnswer:<br \/>\nc\u00b3 &#8211; 7c\u00b2 + 12c = 0<br \/>\nc\u00b2 &#8211; 7c + 12 = 0<br \/>\nc\u00b2 &#8211; 3c &#8211; 4c + 12 = 0<br \/>\nc(c &#8211; 3) &#8211; 4(c &#8211; 3) = 0<br \/>\n(c &#8211; 3)(c &#8211; 4) = 0<br \/>\nc = 3, 4<\/p>\n<p>Question 9.<br \/>\nA box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x &#8211; 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.<br \/>\nAnswer:<br \/>\nx(x &#8211; 1)(x + 9) = 72<br \/>\n(x\u00b2 &#8211; x)(x + 9) = 72<br \/>\nx\u00b3 + 9x\u00b2 &#8211; x\u00b2 &#8211; 9x = 72<br \/>\nx\u00b3 + 8x\u00b2 &#8211; 9x = 72<br \/>\nx\u00b3 + 8x\u00b2 &#8211; 9x &#8211; 72 = 0<br \/>\nx\u00b2(x + 8) &#8211; 9(x + 8) = 0<br \/>\n(x + 8)(x\u00b2 &#8211; 9) = 0<br \/>\nx = -8, x = 3<br \/>\nx = 3<br \/>\nw = x &#8211; 1 = 3 &#8211; 1 = 2 feet<br \/>\nheight = x + 9 = 3 + 9 = 12 feet<\/p>\n<h3><a id=\"Factoring_Polynomials_Completely_7.8_Exercises\"><\/a>Factoring Polynomials Completely 7.8 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat does it mean for a polynomial to be factored completely?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44367\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 1\" width=\"537\" height=\"56\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-1.png 537w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-1-300x31.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to choose which terms to group together when factoring by grouping.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122188\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-2Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"430\" height=\"112\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-2Q.jpg 514w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-2Q-300x78.jpg 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, factor the polynomial by grouping.<\/strong><br \/>\nQuestion 3.<br \/>\nx<sup>3<\/sup> + x<sup>2<\/sup> + 2x + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44368\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 3\" width=\"398\" height=\"145\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-3.png 398w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-3-300x109.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p>\n<p>Question 4.<br \/>\ny<sup>3<\/sup> &#8211; 9y<sup>2<\/sup>+ y &#8211; 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122189\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-4Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"507\" height=\"193\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-4Q.jpg 651w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-4Q-300x114.jpg 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 5.<br \/>\n3z<sup>3<\/sup> + 2z &#8211; 12z<sup>2<\/sup> &#8211; 8<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44369\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 5\" width=\"461\" height=\"171\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-5.png 461w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-5-300x111.png 300w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Question 6.<br \/>\n2s<sup>3<\/sup> &#8211; 27 &#8211; 18s + 3s<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122190\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-6Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"388\" height=\"232\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-6Q.jpg 800w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-6Q-300x179.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-6Q-768x459.jpg 768w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> + xy + 8x + 8y<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44370\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 7\" width=\"412\" height=\"143\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-7.png 412w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-7-300x104.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><\/p>\n<p>Question 8.<br \/>\nq<sup>2<\/sup> + q + 5pq + 5p<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122191\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-8Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"441\" height=\"253\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-8Q.jpg 614w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-8Q-300x172.jpg 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p>Question 9.<br \/>\nm<sup>2<\/sup> &#8211; 3m + mn &#8211; 3n<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44371\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 9\" width=\"465\" height=\"142\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-9.png 465w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-9-300x92.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Question 10.<br \/>\n2a<sup>2<\/sup> + 8ab &#8211; 3a &#8211; 12b<br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-122192\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-10Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"424\" height=\"251\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-10Q.jpg 650w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-10Q-300x178.jpg 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p><strong>In Exercises 11\u201322, factor the polynomial completely.<\/strong><br \/>\nQuestion 11.<br \/>\n2x<sup>3<\/sup> &#8211; 2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44372\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 11\" width=\"323\" height=\"142\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-11.png 323w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-11-300x132.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 12.<br \/>\n36a<sup>4<\/sup> &#8211; 4a<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122193\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-12Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"574\" height=\"184\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-12Q.jpg 796w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-12Q-300x96.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-12Q-768x246.jpg 768w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 13.<br \/>\n2c<sup>2<\/sup> &#8211; 7c + 19<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44373\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 13\" width=\"610\" height=\"290\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-13.png 610w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-13-300x143.png 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><\/p>\n<p>Question 14.<br \/>\nm<sup>2<\/sup> &#8211; 5m &#8211; 35<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122194\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-14Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"608\" height=\"83\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-14Q.jpg 1026w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-14Q-300x41.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-14Q-1024x139.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-14Q-768x104.jpg 768w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Question 15.<br \/>\n6g<sup>3<\/sup> &#8211; 24g<sup>2<\/sup> + 24g<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44374\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 15\" width=\"418\" height=\"139\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-15.png 418w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-15-300x100.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 16.<br \/>\n-15d<sup>3<\/sup> + 21d<sup>2<\/sup> &#8211; 6d<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122195\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-16Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"463\" height=\"402\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-16Q.jpg 689w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-16Q-300x260.jpg 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 17.<br \/>\n3r<sup>5<\/sup> + 3r<sup>4<\/sup> &#8211; 90r<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44375\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 17\" width=\"393\" height=\"105\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-17.png 393w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-17-300x80.png 300w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><\/p>\n<p>Question 18.<br \/>\n5w<sup>4<\/sup> &#8211; 40w<sup>3<\/sup> + 80w<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122197\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-18Q.jpg\" alt=\"\" width=\"649\" height=\"127\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-18Q.jpg 915w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-18Q-300x59.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-18Q-768x150.jpg 768w\" sizes=\"(max-width: 649px) 100vw, 649px\" \/><\/p>\n<p>Question 19.<br \/>\n-4c<sup>4<\/sup> + 8c<sup>3<\/sup> &#8211; 28c<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44376\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 19\" width=\"540\" height=\"236\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-19.png 540w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-19-300x131.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 20.<br \/>\n8t<sup>2<\/sup> + 8t &#8211; 72<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122199\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-20Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"575\" height=\"91\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-20Q.jpg 903w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-20Q-300x48.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-20Q-768x122.jpg 768w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 21.<br \/>\nb<sup>3<\/sup> &#8211; 5b<sup>2<\/sup> &#8211; 4b + 20<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44377\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 21\" width=\"479\" height=\"210\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-21.png 479w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-21-300x132.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 22.<br \/>\nh<sup>3<\/sup> + 4h<sup>2<\/sup> &#8211; 25h &#8211; 100<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122200\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-22Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"466\" height=\"271\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-22Q.jpg 795w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-22Q-300x174.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-22Q-768x445.jpg 768w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p><strong>In Exercises 23\u201328, solve the equation.<\/strong><br \/>\nQuestion 23.<br \/>\n5n<sup>3<\/sup> &#8211; 30n<sup>2<\/sup> + 40n = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44378\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 23\" width=\"452\" height=\"256\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-23.png 452w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-23-300x170.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 24.<br \/>\nk<sup>4<\/sup> &#8211; 100k<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-122201\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-24Q.jpg\" alt=\"ccssanswers.com\/wp-admin\/post.php?post=36561&amp;action=edit\" width=\"666\" height=\"483\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-24Q.jpg 943w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-24Q-300x218.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Solving-Systems-of-Linear-Equations-7.8-24Q-768x557.jpg 768w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><\/p>\n<p>Question 25.<br \/>\nx<sup>3<\/sup> + x<sup>2<\/sup> = 4x + 4<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44379\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 25\" width=\"492\" height=\"484\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-25.png 492w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-25-300x295.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 26.<br \/>\n2t<sup>5<\/sup> + 2t<sup>4<\/sup> &#8211; 144t<sup>3<\/sup> = 0<br \/>\nAnswer:<br \/>\n2t<sup>5<\/sup> + 2t<sup>4<\/sup> &#8211; 144t<sup>3<\/sup> = 0<br \/>\n2t\u00b3(t\u00b2 + t &#8211; 72) = 0<br \/>\nt\u00b2 + t &#8211; 72 = 0<br \/>\nt\u00b2 + 9t &#8211; 8t &#8211; 72 = 0<br \/>\nt(t + 9) &#8211; 8(t + 9) = 0<br \/>\n(t + 9)(t &#8211; 8) = 0<br \/>\nt = 8, -9<\/p>\n<p>Question 27.<br \/>\n12s &#8211; 3s<sup>3<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44380\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 27\" width=\"453\" height=\"290\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-27.png 453w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-27-300x192.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 28.<br \/>\n4y<sup>3<\/sup> &#8211; 7y<sup>2<\/sup> + 28 = 16y<br \/>\nAnswer:<br \/>\n4y\u00b3 &#8211; 7y\u00b2 + 28\u00a0 = 16y<br \/>\n4y\u00b3 &#8211; 7y\u00b2 &#8211; 16y + 28 = 0<br \/>\ny\u00b2(4y &#8211; 7) &#8211; 4(4y &#8211; 7) = 0<br \/>\n(4y &#8211; 7)(y\u00b2 &#8211; 4) = 0<br \/>\n4y &#8211; 7 = 0 or y\u00b2 &#8211; 4 = 0<br \/>\ny = 7\/4 or y\u00b2 = 4<br \/>\ny = 7\/4 or 2<\/p>\n<p><strong>In Exercises 29\u201332, find the x-coordinates of the points where the graph crosses the x-axis.<\/strong><br \/>\nQuestion 29.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36676\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 4\" width=\"134\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44381\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 29\" width=\"550\" height=\"371\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-29.png 550w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-29-300x202.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 30.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36677\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 5\" width=\"164\" height=\"154\" \/><br \/>\nAnswer:<br \/>\ny = -3x<sup>4<\/sup> &#8211; 24x\u00b3 &#8211; 45x\u00b2<br \/>\ny = 0<br \/>\n-3x<sup>4<\/sup> &#8211; 24x\u00b3 &#8211; 45x\u00b2 = 0<br \/>\nx\u00b2(-3x\u00b2 &#8211; 24x &#8211; 45) = 0<br \/>\n-3x\u00b2 &#8211; 24x &#8211; 45 = 0<br \/>\nx\u00b2 + 8x + 15 = 0<br \/>\nx\u00b2 + 3x + 5x + 15 = 0<br \/>\nx(x + 3) + 5(x + 3) = 0<br \/>\n(x + 3)(x + 5) = 0<br \/>\nx = -3, -5<\/p>\n<p>Question 31.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36678\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 6\" width=\"168\" height=\"183\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44382\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 31\" width=\"555\" height=\"459\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-31.png 555w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-31-300x248.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 32.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36679\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 7\" width=\"141\" height=\"192\" \/><br \/>\nAnswer:<br \/>\ny = 4x\u00b3 + 25x\u00b2 &#8211; 56x<br \/>\n4x\u00b3 + 25x\u00b2 &#8211; 56x = 0<br \/>\nx(4x\u00b2 + 25x &#8211; 56) = 0<br \/>\n4x\u00b2 + 25x &#8211; 56 = 0<br \/>\n4x\u00b2 + 32x &#8211; 7x &#8211; 56 = 0<br \/>\n4x(x + 8) &#8211; 7(x + 8) = 0<br \/>\n(x + 8)(4x &#8211; 7) = 0<br \/>\nx = -8, 7\/4<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 33 and 34, describe and correct the error in factoring the polynomial completely.<br \/>\nQuestion 33.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36680\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 8\" width=\"332\" height=\"84\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-8.png 332w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-8-300x76.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44383\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 33\" width=\"466\" height=\"173\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-33.png 466w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-33-300x111.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 34.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36681\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 9\" width=\"330\" height=\"84\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-9.png 330w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-9-300x76.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\nx\u00b3 &#8211; 6x\u00b2 &#8211; 9x + 54<br \/>\n= x\u00b2(x &#8211; 6) &#8211; 9(x &#8211; 6)<br \/>\n= (x &#8211; 6)(x\u00b2 &#8211; 9)<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are building a birdhouse in the shape of a rectangular prism that has a volume of 128 cubic inches. The dimensions of the birdhouse in terms of its width are shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36682\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 10\" width=\"182\" height=\"198\" \/><br \/>\na. Write a polynomial that represents the volume of the birdhouse.<br \/>\nb. What are the dimensions of the birdhouse?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44384\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 35.1\" width=\"583\" height=\"480\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-35.1.png 583w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-35.1-300x247.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44385\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 35.2\" width=\"560\" height=\"439\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-35.2.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-35.2-300x235.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA gift bag shaped like a rectangular prism has a volume of 1152 cubic inches. The dimensions of the gift bag in terms of its width are shown. The height is greater than the width. What are the dimensions of the gift bag?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36683\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 11\" width=\"218\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nV = lwh<br \/>\nV = 1152<br \/>\n1152 = (2w + 4)(w)(18 &#8211; w)<br \/>\n-2w\u00b3 + 36w\u00b2 &#8211; 4w\u00b2 + 72w = 1152<br \/>\n-2w\u00b3 + 32w\u00b2 + 72w = 1152<br \/>\n-w\u00b3 + 16w\u00b2 &#8211; 36w + 576 = 0<br \/>\n-w\u00b2(w &#8211; 16) -36(w &#8211; 16) = 0<br \/>\n(w &#8211; 16)(-w\u00b2 &#8211; 36) = 0<br \/>\nw = 16 or w = -6<br \/>\nw = 16<br \/>\nw = 6 in<br \/>\nl = 16 in<br \/>\nh = 12 in.<\/p>\n<p><strong>In Exercises 37\u201340, factor the polynomial completely.<\/strong><br \/>\nQuestion 37.<br \/>\nx<sup>3<\/sup> + 2x<sup>2<\/sup>y &#8211; x &#8211; 2y<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44386\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 37\" width=\"474\" height=\"212\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-37.png 474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-37-300x134.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 38.<br \/>\n8b<sup>3<\/sup> &#8211; 4b<sup>2<\/sup>a &#8211; 18b + 9a<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n4s<sup>2<\/sup> &#8211; s + 12st &#8211; 3t<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44387\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 39\" width=\"438\" height=\"144\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-39.png 438w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-39-300x99.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<p>Question 40.<br \/>\n6m<sup>3<\/sup> &#8211; 12mn + m<sup>2<\/sup>n &#8211; 2n<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>WRITING<\/strong><br \/>\nIs it possible to find three real solutions of the equation x<sup>3<\/sup> + 2x<sup>2<\/sup> + 3x + 6 = 0? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44388\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 41\" width=\"556\" height=\"309\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-41.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-41-300x167.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nHow can you use the factored form of the polynomial x<sup>4<\/sup> &#8211; 2x<sup>3<\/sup> &#8211; 9x<sup>2<\/sup> + 18x = x(x &#8211; 3)(x + 3)(x &#8211; 2) to find the x-intercepts of the graph of the function?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36684\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-12.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 12\" width=\"258\" height=\"172\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a polynomial of degree 3 that satisfies each of the given conditions.<br \/>\na. is not factorable<br \/>\nb. can be factored by grouping<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44389\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 43\" width=\"561\" height=\"331\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-43.png 561w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-43-300x177.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that if a trinomial cannot be factored as the product of two binomials, then the trinomial is factored completely. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nIn fact, a trinomial ax\u00b2 + bx + c can be factored only if it can be written as the product of two binomials say (ax + n)(x + m)<br \/>\nc = mn<br \/>\nac = pq<br \/>\nb = p + q<br \/>\n= am + n<br \/>\nThe given statement trinomial cannot be factored as the product of two binomials, then the trinomial cannot be factored completely.<\/p>\n<p>Question 45.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe volume (in cubic feet) of a room in the shape of a rectangular prism is represented by 12z<sup>3<\/sup> &#8211; 27z. Find expressions that could represent the dimensions of the room.<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44390\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 45\" width=\"559\" height=\"166\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-45.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-45-300x89.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe width of a box in the shape of a rectangular prism is 4 inches more than the height h. The length is the difference of 9 inches and the height.<br \/>\na. Write a polynomial that represents the volume of the box in terms of its height (in inches).<br \/>\nb. The volume of the box is 180 cubic inches. What are the possible dimensions of the box?<br \/>\nc. Which dimensions result in a box with the least possible surface area? Explain your reasoning.<br \/>\nAnswer:<br \/>\nV = lwh<br \/>\nV = h(h + 4)(9 &#8211; h)<br \/>\nV = h(5h &#8211; h\u00b2 + 36)<br \/>\n= -h\u00b3 + 5h\u00b2 + 36h<br \/>\nV = 180 cu. in<br \/>\n180 = -h\u00b3 + 5h\u00b2 + 36h<br \/>\nh = 5 or 6<br \/>\nThe volume of the box is -h\u00b3 + 5h\u00b2 + 36h.<\/p>\n<p>Question 47.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe volume of a cylinder is given by V = \u03c0r<sup>2<\/sup>h, where r is the radius of the base of the cylinder and h is the height of the cylinder. Find the dimensions of the cylinder.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36685\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 13\" width=\"169\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44391\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 47\" width=\"560\" height=\"642\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-47.png 560w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-47-262x300.png 262w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nFactor the polynomial x<sup>5<\/sup> &#8211; x<sup>4<\/sup> &#8211; 5x<sup>3<\/sup> + 5x<sup>2<\/sup> + 4x &#8211; 4 completely.<br \/>\nAnswer:<br \/>\nx<sup>5<\/sup> &#8211; x<sup>4<\/sup> &#8211; 5x<sup>3<\/sup> + 5x<sup>2<\/sup> + 4x &#8211; 4<br \/>\nx<sup>4<\/sup>(x &#8211; 1) &#8211; 5x\u00b2(x &#8211; 1) + 4(x &#8211; 1)<br \/>\n(x &#8211; 1)(x<sup>4 <\/sup>&#8211; 5x\u00b2 + 4)<\/p>\n<p>Question 49.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind a value for w so that the equation has (a) two solutions and (b) three solutions. Explain your reasoning. 5x<sup>3<\/sup> + wx<sup>2<\/sup> + 80x = 0<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44392\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-49.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 49.1\" width=\"556\" height=\"394\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-49.1.png 556w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-49.1-300x213.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44393\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-49.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 49.2\" width=\"596\" height=\"417\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-49.2.png 596w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-49.2-300x210.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the system of linear equations by graphing.<\/strong><br \/>\nQuestion 50.<br \/>\ny = x &#8211; 4<br \/>\ny = -2x + 2<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195819 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Answer-Key-Factoring-Polynomials-Completely-7.8-Exercises_50.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Answer Key Factoring Polynomials Completely 7.8 Exercises_50\" width=\"662\" height=\"506\" \/><\/p>\n<p>Question 51.<br \/>\ny = \\(\\frac{1}{2}\\)x + 2<br \/>\ny = 3x &#8211; 3<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44394\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 51\" width=\"455\" height=\"358\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-51.png 455w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-51-300x236.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 52.<br \/>\n5x &#8211; y = 12<br \/>\n\\(\\frac{1}{4}\\)x + y = 9<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195818 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Answer-Key-Factoring-Polynomials-Completely-7.8-Exercises_52.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Answer Key Factoring Polynomials Completely 7.8 Exercises_52\" width=\"640\" height=\"596\" \/><\/p>\n<p>Question 53.<br \/>\nx = 3y<br \/>\ny &#8211; 10 = 2x<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44395\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 53\" width=\"494\" height=\"513\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-53.png 494w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-53-289x300.png 289w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p><strong>Graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 54.<br \/>\nf(x) = 5<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195817 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Answer-Key-Factoring-Polynomials-Completely-7.8-Exercises_54.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Answer Key Factoring Polynomials Completely 7.8 Exercises_54\" width=\"535\" height=\"596\" \/><\/p>\n<p>Question 55.<br \/>\ny = 9 (\\(\\frac{1}{3}\\))<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44396\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 55\" width=\"576\" height=\"471\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-55.png 576w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-55-300x245.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 56.<br \/>\ny = -3(0.5)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-195816 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Answer-Key-Factoring-Polynomials-Completely-7.8-Exercises_56.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Answer Key Factoring Polynomials Completely 7.8 Exercises_56\" width=\"780\" height=\"548\" \/><\/p>\n<p>Question 57.<br \/>\nf(x) = -3(4)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-44397\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring 7.8 Question 57\" width=\"564\" height=\"495\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-57.png 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-7.8-Question-57-300x263.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Performance_Task:_The_View_Matters\"><\/a>Polynomial Equations and Factoring Performance Task: The View Matters<\/h3>\n<p><strong>7.5 \u2013 7.8 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\nfactoring by grouping, p. 404<br \/>\nfactored completely, p. 404<\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 7.5<br \/>\nFactoring x<sup>2<\/sup> + bx + c When c Is Positive, p. 386<br \/>\nFactoring x<sup>2<\/sup> + bx + c When cIs Negative, p. 387<\/p>\n<p>Section 7.6<br \/>\nFactoring ax<sup>2<\/sup> + bx + c When ac Is Positive, p. 392<br \/>\nFactoring ax<sup>2<\/sup> + bx + c When ac Is Negative, p. 393<\/p>\n<p>Section 7.7<br \/>\nDifference of Two Squares Pattern, p. 398<br \/>\nPerfect SquareTrinomial Pattern, p. 399<\/p>\n<p>Section 7.8<br \/>\nFactoring by Grouping, p. 404<br \/>\nFactoring Polynomials Completely, p. 404<\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nHow are the solutions of Exercise 29 on page 389 related to the graph of y = m<sup>2<\/sup> + 3m + 2?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nThe equation in part (b) of Exercise 47 on page 390 has two solutions. Are both solutions of the equation reasonable in the context of the problem? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task: The View Matters<\/strong><\/p>\n<p>The way an equation or expression is written can help you interpret and solve problems. Which representation would you rather have when trying to solve for specific information? Why?<br \/>\nTo explore the answers to these questions and more, go to<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36686\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-14.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 7 Polynomial Equations and Factoring 7.8 14\" width=\"412\" height=\"244\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-14.png 412w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-7-Polynomial-Equations-and-Factoring-7.8-14-300x178.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><\/p>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Chapter_Review\"><\/a>Polynomial Equations and Factoring Chapter Review<\/h3>\n<p><strong>7.1 Adding and Subtracting Polynomials<\/strong><\/p>\n<p>Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.<br \/>\nQuestion 1.<br \/>\n6 + 2x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n6 + 2x<sup>2<\/sup><br \/>\nThe polynomial in standard form is 2x\u00b2 + 6<br \/>\nThe degree of the polynomial is 2<br \/>\ncoefficient is 2<br \/>\nThere are 2 terms in the polynomial so it is binomial.<\/p>\n<p>Question 2.<br \/>\n-3p<sup>3<\/sup> + 5p<sup>6<\/sup> &#8211; 4<br \/>\nAnswer:<br \/>\nThe polynomial in standard form is 5p<sup>6<\/sup> -3p<sup>3 <\/sup>&#8211; 4<br \/>\nThe degree of the polynomial is 6<br \/>\nthe coefficient is 5, -3<br \/>\nThere are 3 terms in the polynomial so it is a trinomial.<\/p>\n<p>Question 3.<br \/>\n9x<sup>7<\/sup> &#8211; 6x<sup>2<\/sup> + 13x<sup>5<\/sup><br \/>\nAnswer:<br \/>\nThe polynomial in standard form is 9x<sup>7<\/sup> + 13x<sup>5 <\/sup>&#8211; 6x<sup>2<\/sup><br \/>\nThe degree of the polynomial is 7<br \/>\nthe coefficient is 9, 13 and -6<br \/>\nThere are 3 terms in the polynomial so it is a trinomial.<\/p>\n<p>Question 4.<br \/>\n-12y + 8y<sup>3<\/sup><br \/>\nAnswer:<br \/>\nThe polynomial in standard form is 8y<sup>3 <\/sup>-12y<br \/>\nThe degree of the polynomial is 3<br \/>\nthe coefficient is 8, -12<br \/>\nThere are 2 terms in the polynomial so it is binomial.<\/p>\n<p><strong>Find the sum or difference.<\/strong><br \/>\nQuestion 5.<br \/>\n(3a + 7) + (a &#8211; 1)<br \/>\nAnswer:<br \/>\n(3a + 7) + (a &#8211; 1)<br \/>\n3a + 7 + a &#8211; 1<br \/>\n3a + a + 7 &#8211; 1<br \/>\n4a + 6<br \/>\n(3a + 7) + (a &#8211; 1) = 4a + 6<\/p>\n<p>Question 6.<br \/>\n(x<sup>2<\/sup> + 6x &#8211; 5) + (2x<sup>2<\/sup> + 15)<br \/>\nAnswer:<br \/>\n(x<sup>2<\/sup> + 6x &#8211; 5) + (2x<sup>2<\/sup> + 15)<br \/>\nx<sup>2<\/sup> + 6x &#8211; 5 + 2x<sup>2<\/sup> + 15<br \/>\n3x\u00b2 + 6x + 10<\/p>\n<p>Question 7.<br \/>\n(-y<sup>2<\/sup> + y + 2) &#8211; (y<sup>2<\/sup> &#8211; 5y &#8211; 2)<br \/>\nAnswer:<br \/>\n(-y<sup>2<\/sup> + y + 2) &#8211; (y<sup>2<\/sup> &#8211; 5y &#8211; 2)<br \/>\n-y<sup>2<\/sup> + y + 2 &#8211; y<sup>2<\/sup> + 5y + 2<br \/>\n-2y\u00b2 + 6y + 4<\/p>\n<p>Question 8.<br \/>\n(p + 7) &#8211; (6p<sup>2<\/sup> + 13p)<br \/>\nAnswer:<br \/>\n(p + 7) &#8211; (6p<sup>2<\/sup> + 13p)<br \/>\np + 7 &#8211; 6p<sup>2<\/sup> + 13p<br \/>\n-6p\u00b2 + 14p + 7<\/p>\n<p><strong>7.2 Multiplying Polynomials<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 9.<br \/>\n(x + 6)(x &#8211; 4)<br \/>\nAnswer:<br \/>\n(x + 6)(x &#8211; 4)<br \/>\n= x(x &#8211; 4) + 6(x &#8211; 4)<br \/>\n= x\u00b2 &#8211; 4x + 6x &#8211; 24<br \/>\n= x\u00b2 + 2x &#8211; 24<\/p>\n<p>Question 10.<br \/>\n(y &#8211; 5)(3y + 8)<br \/>\nAnswer:<br \/>\n(y &#8211; 5)(3y + 8)<br \/>\n= y(3y + 8) &#8211; 5(3y + 8)<br \/>\n= 3y\u00b2 + 8y &#8211; 15y &#8211; 40<br \/>\n= 3y\u00b2 &#8211; 7y &#8211; 40<\/p>\n<p>Question 11.<br \/>\n(x + 4)(x<sup>2<\/sup> + 7x)<br \/>\nAnswer:<br \/>\n(x + 4)(x<sup>2<\/sup> + 7x)<br \/>\n= x(x<sup>2<\/sup> + 7x) + 4(x<sup>2<\/sup> + 7x)<br \/>\n= x\u00b3 + 7x\u00b2 + 4x\u00b2 + 28x<br \/>\n= x\u00b3 + 11x\u00b2 + 28x<\/p>\n<p>Question 12.<br \/>\n(-3y + 1)(4y<sup>2<\/sup> &#8211; y &#8211; 7)<br \/>\nAnswer:<br \/>\n(-3y + 1)(4y<sup>2<\/sup> &#8211; y &#8211; 7)<br \/>\n= -3y(4y<sup>2<\/sup> &#8211; y &#8211; 7) + 1(4y<sup>2<\/sup> &#8211; y &#8211; 7)<br \/>\n= 12y\u00b3 + 3y\u00b2 + 21y + 4y\u00b2 &#8211; y &#8211; 7<br \/>\n= 12y\u00b3 + 7y\u00b2 + 20y &#8211; 7<\/p>\n<p><strong>7.3 Special Products of Polynomials<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 13.<br \/>\n(x + 9)(x &#8211; 9)<br \/>\nAnswer:<br \/>\n(x + 9)(x &#8211; 9)<br \/>\n(x + 9)(x &#8211; 9) = (x)\u00b2 &#8211; (9)\u00b2<br \/>\n= x\u00b2 &#8211; 81<\/p>\n<p>Question 14.<br \/>\n(2y + 4)(2y &#8211; 4)<br \/>\nAnswer:<br \/>\n(2y + 4)(2y &#8211; 4) = (2x)\u00b2 &#8211; (4)\u00b2<br \/>\n= 4x\u00b2 &#8211; 16<\/p>\n<p>Question 15.<br \/>\n( p + 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(p + 4)\u00b2 = p\u00b2 + 4\u00b2 + 2.p.4<br \/>\n= p\u00b2 + 16 + 8p<br \/>\n= p\u00b2 + 8p + 16<\/p>\n<p>Question 16.<br \/>\n(-1+ 2d )<sup>2<\/sup><br \/>\nAnswer:<br \/>\n(-1+ 2d)\u00b2 = (2d &#8211; 1)\u00b2<br \/>\n(2d &#8211; 1)\u00b2 = (2d)\u00b2 + 1\u00b2 &#8211; 2(2d)(1)<br \/>\n= 4d\u00b2 + 1 &#8211; 4d<\/p>\n<p><strong>7.4 Solving Polynomial Equations in Factored Form (pp. 377\u2013382)<\/strong><\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 17.<br \/>\nx<sup>2<\/sup> + 5x = 0<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> + 5x = 0<br \/>\nx(x + 5) = 0<br \/>\nx = 0 or x+ 5 = 0<br \/>\nx = 0 or x = -5<br \/>\nSo, x = 0, -5<\/p>\n<p>Question 18.<br \/>\n(z + 3)(z &#8211; 7) = 0<br \/>\nAnswer:<br \/>\n(z + 3)(z &#8211; 7) = 0<br \/>\nz + 3 = 0 or z &#8211; 7 = 0<br \/>\nz = -3 or z = 7<\/p>\n<p>Question 19.<br \/>\n(b + 13)<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n(b + 13)<sup>2<\/sup> = 0<br \/>\nb + 13 = 0<br \/>\nb = -13<\/p>\n<p>Question 20.<br \/>\n2y(y &#8211; 9)(y + 4) = 0<br \/>\nAnswer:<br \/>\n2y(y &#8211; 9)(y + 4) = 0<br \/>\n2y = 0 or y &#8211; 9 = 0 or y + 4 = 0<br \/>\ny = 0 or y = 9 or y = -4<br \/>\nSo, y = 0, 9, -4<\/p>\n<p><strong>7.5 Factoring x<sup>2<\/sup> + bx + c(pp. 385\u2013390)<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 21.<br \/>\np<sup>2<\/sup> + 2p &#8211; 35<br \/>\nAnswer:<br \/>\np<sup>2<\/sup> + 2p &#8211; 35<br \/>\n7 \u00d7 5 = 35<br \/>\np\u00b2 + 7p &#8211; 5p &#8211; 35<br \/>\np(p + 7) &#8211; 5(p + 7)<br \/>\n(p &#8211; 5)(p + 7)<br \/>\np &#8211; 5 = 0 or p + 7 = 0<br \/>\np = 5 or p = -7<\/p>\n<p>Question 22.<br \/>\nb<sup>2<\/sup> + 18b + 80<br \/>\nAnswer:<br \/>\nb<sup>2<\/sup> + 18b + 80<br \/>\nb\u00b2 + 10b + 8b + 80<br \/>\nb(b + 10) + 8(b + 10)<br \/>\n(b + 10)(b + 8)<br \/>\nb + 10 = 0 or b + 8 = 0<br \/>\nb = -10, -8<\/p>\n<p>Question 23.<br \/>\nz<sup>2<\/sup> &#8211; 4z &#8211; 21<br \/>\nAnswer:<br \/>\nz<sup>2<\/sup> &#8211; 4z &#8211; 21<br \/>\nz\u00b2 &#8211; 7z + 3z &#8211; 21<br \/>\nz(z &#8211; 7) + 3(z &#8211; 7)<br \/>\n(z &#8211; 7)(z + 3)<br \/>\nz = 7, -3<\/p>\n<p>Question 24.<br \/>\nx<sup>2<\/sup> &#8211; 11x + 28<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> &#8211; 11x + 28<br \/>\nx\u00b2 &#8211; 7x &#8211; 4x + 28<br \/>\nx(x &#8211; 7) &#8211; 4(x &#8211; 7)<br \/>\n(x &#8211; 4)(x &#8211; 7)<br \/>\nx = 4, 7<\/p>\n<p><strong>7.6 Factoring ax<sup>2<\/sup> + bx + c (pp. 391\u2013396)<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 25.<br \/>\n3t<sup>2<\/sup> + 16t &#8211; 12<br \/>\nAnswer:<br \/>\n3t<sup>2<\/sup> + 16t &#8211; 12<br \/>\n3t\u00b2 + 18t &#8211; 2t &#8211; 12<br \/>\n3t(t + 6) &#8211; 2(t + 6)<br \/>\n(t + 6)(3t &#8211; 2)<br \/>\nt = 6 or t = 2\/3<\/p>\n<p>Question 26.<br \/>\n-5y<sup>2<\/sup> &#8211; 22y &#8211; 8<br \/>\nAnswer:<br \/>\n-5y<sup>2<\/sup> &#8211; 22y &#8211; 8<br \/>\n-5y\u00b2 &#8211; 20y &#8211; 2y &#8211; 8<br \/>\n-5y(y + 4) &#8211; 2(y + 4)<br \/>\n(y + 4)(-5y &#8211; 2)<br \/>\ny + 4 = 0 or -5y &#8211; 2 = 0<br \/>\ny = -4 or y = -2\/5<br \/>\ny = 4, -2\/5<\/p>\n<p>Question 27.<br \/>\n6x<sup>2<\/sup> + 17x + 7<br \/>\nAnswer:<br \/>\n6x<sup>2<\/sup> + 17x + 7<br \/>\n7 \u00d7 6 = 42<br \/>\n6x\u00b2 + 3x + 14x + 7<br \/>\n3x(2x + 1) + 7(2x + 1)<br \/>\n(3x + 7)(2x + 1)<br \/>\nx = -7\/3, -1\/2<\/p>\n<p>Question 28.<br \/>\n-2y<sup>2<\/sup> + 7y &#8211; 6<br \/>\nAnswer:<br \/>\n-2y<sup>2<\/sup> + 7y &#8211; 6<br \/>\n-2y\u00b2 + 3y + 4y &#8211; 6<br \/>\n-y(2y &#8211; 3) + 2(2y &#8211; 3)<br \/>\n(2y &#8211; 3)(-y + 2)<br \/>\ny = 3\/2, -2<\/p>\n<p>Question 29.<br \/>\n3z<sup>2<\/sup> + 26z &#8211; 9<br \/>\nAnswer:<br \/>\n3z<sup>2<\/sup> + 26z &#8211; 9<br \/>\n3z<sup>2<\/sup> + 27 z -1z &#8211; 9<br \/>\n3z(z + 9) -1(z + 9)<br \/>\n(3z &#8211; 1)(z + 9)<br \/>\nz = -9, 1\/3<\/p>\n<p>Question 30.<br \/>\n10a<sup>2<\/sup> &#8211; 13a &#8211; 3<br \/>\nAnswer:<br \/>\n10a<sup>2<\/sup> &#8211; 13a &#8211; 3<br \/>\n10a<sup>2<\/sup> &#8211; 15a + 2a &#8211; 3<br \/>\n5a(2a &#8211; 3) + 1(2a &#8211; 3)<br \/>\n(2a &#8211; 3)(5a + 1)<br \/>\n2a &#8211; 3 = 0 or 5a + 1 = 0<br \/>\n2a = 3 or 5a = -1<br \/>\na = 3\/2, -1\/5<\/p>\n<p><strong>7.7 Factoring Special Products (pp. 397\u2013402)<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 31.<br \/>\nx<sup>2<\/sup> &#8211; 9<br \/>\nAnswer: x<sup>2<\/sup> &#8211; 9 = x<sup>2<\/sup> &#8211; 3\u00b2 = (x + 3)(x &#8211; 3)<\/p>\n<p>Question 32.<br \/>\ny<sup>2<\/sup> &#8211; 100<br \/>\nAnswer: y<sup>2<\/sup> &#8211; 100 = y<sup>2<\/sup> &#8211; 10\u00b2 = (y + 10)(y &#8211; 10)<\/p>\n<p>Question 33.<br \/>\nz<sup>2<\/sup> &#8211; 6z + 9<br \/>\nAnswer: z<sup>2<\/sup> &#8211; 6z + 9 = (z &#8211; 3)\u00b2<\/p>\n<p>Question 34.<br \/>\nm<sup>2<\/sup> + 16m + 64<br \/>\nAnswer: m<sup>2<\/sup> + 16m + 64 = (m + 8)\u00b2<\/p>\n<p><strong>7.8 Factoring Polynomials Completely (pp. 403\u2013408)<\/strong><\/p>\n<p><strong>Factor the polynomial completely.<\/strong><br \/>\nQuestion 35.<br \/>\nn<sup>3<\/sup> &#8211; 9n<br \/>\nAnswer:<br \/>\nn<sup>3<\/sup> &#8211; 9n<br \/>\nn(n\u00b2 &#8211; 9)<br \/>\nn = 0 or n\u00b2 &#8211; 9 = 0<br \/>\nn = 0 or n\u00b2 = 9<br \/>\nn = 0, 3<\/p>\n<p>Question 36.<br \/>\nx<sup>2<\/sup> &#8211; 3x + 4ax &#8211; 12a<br \/>\nAnswer:<br \/>\nx<sup>2<\/sup> &#8211; 3x + 4ax &#8211; 12a<br \/>\nx(x &#8211; 3) + 4a(x &#8211; 3)<br \/>\n(x &#8211; 3)(x + 4a) = 0<br \/>\nx &#8211; 3 = 0 or x + 4a = 0<br \/>\nx = 3 or a = -4a<\/p>\n<p>Question 37.<br \/>\n2x<sup>4<\/sup> + 2x<sup>3<\/sup> &#8211; 20x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n2x<sup>4<\/sup> + 2x<sup>3<\/sup> &#8211; 20x<sup>2<\/sup><br \/>\n2x\u00b2(x\u00b2 + x &#8211; 10)<br \/>\n2x\u00b2 = 0 or x\u00b2 + x &#8211; 10 = 0<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 38.<br \/>\n3x<sup>3<\/sup> &#8211; 9x<sup>2<\/sup> &#8211; 54x = 0<br \/>\nAnswer:<br \/>\n3x<sup>3<\/sup> &#8211; 9x<sup>2<\/sup> &#8211; 54x = 0<br \/>\n3x(x\u00b2 &#8211; 3x &#8211; 18) = 0<br \/>\nx\u00b2 &#8211; 3x &#8211; 18 = 0<br \/>\nx\u00b2 &#8211; 6x + 3x &#8211; 18 = 0<br \/>\nx(x &#8211; 6) + 3(x &#8211; 6) = 0<br \/>\n(x + 3)(x &#8211; 6) = 0<br \/>\nx = -3, 6<\/p>\n<p>Question 39.<br \/>\n16x<sup>2<\/sup> &#8211; 36 = 0<br \/>\nAnswer:<br \/>\n16x<sup>2<\/sup> &#8211; 36 = 0<br \/>\n4(4x\u00b2 &#8211; 9) = 0<br \/>\n4x\u00b2 &#8211; 9 = 0<br \/>\n4x\u00b2 = 9<br \/>\nx\u00b2 = 9\/4<br \/>\nx = 3\/2<\/p>\n<p>Question 40.<br \/>\nz<sup>3<\/sup> + 3z<sup>2<\/sup> &#8211; 25z &#8211; 75 = 0<br \/>\nAnswer:<br \/>\nz<sup>3<\/sup> + 3z<sup>2<\/sup> &#8211; 25z &#8211; 75 = 0<br \/>\nz\u00b2(z + 3) &#8211; 25(z + 3) = 0<br \/>\n(z + 3)(z\u00b2 &#8211; 25) = 0<br \/>\nz = -3 or z\u00b2 = 25<br \/>\nz = -3, 5<\/p>\n<p>Question 41.<br \/>\nA box in the shape of a rectangular prism has a volume of 96 cubic feet. The box has a length of (x + 8) feet, a width of x feet, and a height of (x &#8211; 2) feet. Find the dimensions of the box.<br \/>\nAnswer:<br \/>\nl = x + 8<br \/>\nw = x<br \/>\nh = x &#8211; 2<br \/>\nV = lbh<br \/>\n96 = (x + 8)(x)(x &#8211; 2)<br \/>\n(x + 8)(x\u00b2 &#8211; 2x) = 96<br \/>\nx\u00b3 &#8211; 2x\u00b2 + 8x\u00b2 &#8211; 16x = 96<br \/>\nx\u00b3 + 6x\u00b2 &#8211; 16x &#8211; 96 = 0<br \/>\n(x + 6)(x + 4)(x &#8211; 4)<br \/>\nx = -6, -4, 4<br \/>\nx =-6 \u21d2 -6 + 8 = 2<br \/>\nlength = x + 8<br \/>\nw = x \u21d2 -6<br \/>\nh = x &#8211; 2 \u21d2 -6 &#8211; 2 = -8<br \/>\nx =-4 \u21d2 -4 + 8 = 4<br \/>\nlength = x + 8<br \/>\nw = x \u21d2 -4<br \/>\nh = x &#8211; 2 \u21d2 -4 &#8211; 2 = -6<br \/>\nx =4 \u21d2 4 + 8 = 12<br \/>\nlength = x + 8<br \/>\nw = x \u21d2 4<br \/>\nh = x &#8211; 2 \u21d2 4 &#8211; 2 = 2<\/p>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Chapter_Test\"><\/a>Polynomial Equations and Factoring Chapter Test<\/h3>\n<p>Find the sum or difference. Then identify the degree of the sum or difference and classify it by the number of terms.<br \/>\nQuestion 1.<br \/>\n(-2p + 4) &#8211; (p<sup>2<\/sup> &#8211; 6p + 8)<br \/>\nAnswer:<br \/>\n(-2p + 4) &#8211; (p<sup>2<\/sup> &#8211; 6p + 8)<br \/>\n= -2p + 4 &#8211; p<sup>2<\/sup> + 6p &#8211; 8<br \/>\n= -p\u00b2 &#8211; 2p + 6p + 4 &#8211; 8<br \/>\n= -p\u00b2 + 4p &#8211; 4<\/p>\n<p>Question 2.<br \/>\n(9c<sup>6<\/sup> &#8211; 5b<sup>4<\/sup>) &#8211; (4c<sup>6<\/sup> &#8211; 5b<sup>4<\/sup>)<br \/>\nAnswer:<br \/>\n(9c<sup>6<\/sup> &#8211; 5b<sup>4<\/sup>) &#8211; (4c<sup>6<\/sup> &#8211; 5b<sup>4<\/sup>)<br \/>\n= 9c<sup>6<\/sup> &#8211; 5b<sup>4<\/sup>\u00a0&#8211; 4c<sup>6<\/sup> + 5b<sup>4<br \/>\n<\/sup>= 9c<sup>6<\/sup> &#8211; 4c<sup>6<\/sup> + 5b<sup>4 <\/sup>&#8211; 5b<sup>4<\/sup><br \/>\n= 5c<sup>6<\/sup><\/p>\n<p>Question 3.<br \/>\n(4s<sup>4<\/sup> + 2st + t) + (2s<sup>4<\/sup> &#8211; 2st &#8211; 4t)<br \/>\nAnswer:<br \/>\n(4s<sup>4<\/sup> + 2st + t) + (2s<sup>4<\/sup> &#8211; 2st &#8211; 4t)<br \/>\n= 4s<sup>4<\/sup> + 2st + t + 2s<sup>4<\/sup> &#8211; 2st &#8211; 4t<br \/>\n= 6s<sup>4<\/sup> + 2st &#8211; 2st + t &#8211; 4t<br \/>\n= 6s<sup>4<\/sup> &#8211; 3t<\/p>\n<p>Find the product.<br \/>\nQuestion 4.<br \/>\n(h &#8211; 5)(h &#8211; 8)<br \/>\nAnswer:<br \/>\n(h &#8211; 5)(h &#8211; 8)<br \/>\n= h(h &#8211; 8) &#8211; 5(h &#8211; 8)<br \/>\n= h\u00b2 &#8211; 8h &#8211; 5h + 40<br \/>\n= h\u00b2 -13h + 40<\/p>\n<p>Question 5.<br \/>\n(2w &#8211; 3)(3w + 5)<br \/>\nAnswer:<br \/>\n(2w &#8211; 3)(3w + 5)<br \/>\n= 2w(3w + 5) &#8211; 3(3w + 5)<br \/>\n= 6w\u00b2 + 10w &#8211; 9w &#8211; 15<\/p>\n<p>Question 6.<br \/>\n(z + 11)(z &#8211; 11)<br \/>\nAnswer:<br \/>\n(z + 11)(z &#8211; 11)<br \/>\n= z(z &#8211; 11) + 11(z &#8211; 11)<br \/>\n= z\u00b2 &#8211; 11z + 11z &#8211; 121<br \/>\n= z\u00b2 &#8211; 121<\/p>\n<p>Question 7.<br \/>\nExplain how you can determine whether a polynomial is a perfect square trinomial.<br \/>\nAnswer: A polynomial is a perfect square trinomial if the first and last terms are perfect squares, and the middle term&#8217;s coefficient is twice the product of the square roots of the first and last terms.<\/p>\n<p>Question 8.<br \/>\nIs 18 a polynomial? Explain your reasoning.<br \/>\nAnswer:<br \/>\n2z<sup>4<\/sup>, 3y\u00b3<br \/>\nSo, yes 18 is a polynomial.<br \/>\n18x<sup>0<\/sup> = 1<\/p>\n<p>Factor the polynomial completely.<br \/>\nQuestion 9.<br \/>\ns<sup>2<\/sup> &#8211; 15s + 50<br \/>\nAnswer:<br \/>\ns\u00b2 &#8211; 15s + 50<br \/>\n= s\u00b2 &#8211; 5s &#8211; 10s + 50<br \/>\n= s(s &#8211; 5) &#8211; 10(s &#8211; 5)<br \/>\n= (s &#8211; 5)(s &#8211; 10)<br \/>\ns &#8211; 5 = 0 or s &#8211; 10 = 0<br \/>\ns = 5 or s = 10<\/p>\n<p>Question 10.<br \/>\nh<sup>3<\/sup> + 2h<sup>2<\/sup> &#8211; 9h &#8211; 18<br \/>\nAnswer:<br \/>\nh<sup>3<\/sup> + 2h<sup>2<\/sup> &#8211; 9h &#8211; 18<br \/>\n= h\u00b2(h + 2) -2h(h + 2)<br \/>\n= (h\u00b2 &#8211; 2h)(h + 2)<br \/>\nh\u00b2 &#8211; 2h = 0 or h + 2 = 0<br \/>\nh\u00b2 = 2h or h = -2<br \/>\nh = 2 or h = -2<\/p>\n<p>Question 11.<br \/>\n-5k<sup>2<\/sup> &#8211; 22k + 15<br \/>\nAnswer:<br \/>\n-5k<sup>2<\/sup> &#8211; 22k + 15<br \/>\n-5k\u00b2 &#8211; 25k + 3k + 15<br \/>\n-5k(k + 5) + 3(k + 5)<br \/>\n(-5k + 3)(k + 5)<\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 12.<br \/>\n(n &#8211; 1)(n + 6)(n + 5) = 0<br \/>\nAnswer:<br \/>\n(n &#8211; 1)(n + 6)(n + 5) = 0<br \/>\nn &#8211; 1 = 0 or n + 6 = 0 or n + 5 = 0<br \/>\nn = 1 or n = -6 or n = -5<\/p>\n<p>Question 13.<br \/>\nd<sup>2<\/sup> + 14d + 49 = 0<br \/>\nAnswer:<br \/>\nd<sup>2<\/sup> + 14d + 49 = 0<br \/>\nd\u00b2 + 7d + 7d + 49 = 0<br \/>\nd(d + 7) + 7(d + 7) = 0<br \/>\n(d + 7)(d + 7) = 0<br \/>\nd = -7<\/p>\n<p>Question 14.<br \/>\n6x<sup>4<\/sup> + 8x<sup>2<\/sup> = 26x<sup>3<\/sup><br \/>\nAnswer:<br \/>\n6x<sup>4<\/sup> + 8x<sup>2<\/sup> = 26x<sup>3<\/sup><br \/>\nx\u00b2(6x\u00b2 + 8) = (26x)x\u00b2<br \/>\n6x\u00b2 + 8 = 26x<br \/>\n6x\u00b2 + 8 &#8211; 26x = 0<br \/>\n3x\u00b2 + 4 &#8211; 13x = 0<br \/>\n3x\u00b2 &#8211; 13x + 4 = 0<br \/>\n3x\u00b2 &#8211; 12x &#8211; 1x + 4 = 0<br \/>\n3x(x &#8211; 4) -1(x &#8211; 4) = 0<br \/>\n(x &#8211; 4)(3x &#8211; 1) = 0<br \/>\nx &#8211; 4 = 0 or 3x &#8211; 1 = 0<br \/>\nx = 4 or 3x = 1<br \/>\nx = 1\/3 or 4<\/p>\n<p>Question 15.<br \/>\nThe expression \u03c0(r &#8211; 3)<sup>2<\/sup> represents the area covered by the hour hand on a clock in one rotation, where r is the radius of the entire clock. Write a polynomial in standard form that represents the area covered by the hour hand in one rotation.<br \/>\nAnswer:<br \/>\n(r &#8211; 3)<sup>2<\/sup> can be written as (r &#8211; 3)(r &#8211; 3).<br \/>\nr(r &#8211; 3) &#8211; 3(r &#8211; 3)<br \/>\nr\u00b2 &#8211; 3r &#8211; 3r + 9<br \/>\nr\u00b2 &#8211; 6r + 9<br \/>\n\u03c0(r\u00b2 &#8211; 6r + 9)<\/p>\n<p>Question 16.<br \/>\nA magician\u2019s stage has a trapdoor.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36687\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ct-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring ct 1\" width=\"216\" height=\"186\" \/><br \/>\na. The total area (in square feet) of the stage can be represented by x<sup>2<\/sup> + 27x + 176. Write an expression for the width of the stage.<br \/>\nb. Write an expression for the perimeter of the stage.<br \/>\nc. The area of the trapdoor is 10 square feet. Find the value of x.<br \/>\nd. The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. Does this stage satisfy his requirement? Explain.<br \/>\nAnswer:<br \/>\na. x<sup>2<\/sup> + 27x + 176<br \/>\nx\u00b2 + 16 + 11x + 176<br \/>\nx(x + 16) + 11(x +16)<br \/>\n(x + 16)(x + 11)<br \/>\nAs the length is (x + 16) the width is area\/length<br \/>\nSo, the width is x + 11.<br \/>\nb. The total area (in square feet) of the stage can be represented by x<sup>2<\/sup> + 27x + 176.<br \/>\n2(x + 16 + x + 11) or 2(2x + 27)<br \/>\nSo, the perimeter of the stage is 2(x + 16 + x + 11) or 2(2x + 27).<br \/>\nc. The area of the trapdoor is 10 square feet.<br \/>\nArea = 2x(x + 1\/2)<br \/>\n2x(x + 1\/2) = 10<br \/>\n2x\u00b2 + x &#8211; 10 = 0<br \/>\n2x\u00b2 + 5x &#8211; 4x &#8211; 10 = 0<br \/>\nx(2x + 5) -2(2x + 5) = 0<br \/>\n(2x + 5)(x &#8211; 2)<br \/>\n2x + 5 = 0 or x &#8211; 2 = 0<br \/>\nx = -5\/2 or x = 2<br \/>\nd. x<sup>2<\/sup> + 27x + 176 = 20(2x\u00b2 + x &#8211; 10)<br \/>\nThe expression for area of stage becomes x<sup>2<\/sup> + 27x + 176 = 40x\u00b2 + 20x &#8211; 200<br \/>\n39x\u00b2\u00a0 &#8211; 17x &#8211; 376 = 0<br \/>\n\u221a(b\u00b2 &#8211; 4ac = \u221a(-17)\u00b2 -4(39)(-376)<br \/>\nThe discriminant is a positive value.<br \/>\nThe equation will have real roots stating that the stage satisfies his requirements.<\/p>\n<p>Question 17.<br \/>\nWrite a polynomial equation in factored form that has three positive roots.<br \/>\nAnswer:<br \/>\nf(x) = a(x &#8211; h)(x &#8211; k)(x &#8211; r)<br \/>\nwhere a, h, k and r are constants<\/p>\n<p>Question 18.<br \/>\nYou are jumping on a trampoline. For one jump, your height y (in feet) above the trampoline after t seconds can be represented by y = -16t<sup>2<\/sup> + 24t. How many seconds are you in the air?<br \/>\nAnswer:<br \/>\ny = -16t<sup>2<\/sup> + 24t<br \/>\n-8t(2t &#8211; 3) = 0<br \/>\n-8t = 0 or 2t &#8211; 3 = 0<br \/>\nt = 0 or t = 3\/2<br \/>\nSo, t = 0, 3\/2<\/p>\n<p>Question 19.<br \/>\nA cardboard box in the shape of a rectangular prism has the dimensions shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36688\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ct-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 7 Polynomial Equations and Factoring ct 2\" width=\"291\" height=\"113\" \/><br \/>\na. Write a polynomial that represents the volume of the box.<br \/>\nb. The volume of the box is 60 cubic inches. What are the length, width, and height of the box?<br \/>\nAnswer:<br \/>\nl = (x + 6) inch<br \/>\nb = (x &#8211; 2) inch<br \/>\nh = (x &#8211; 1) inch<br \/>\nV = lbh<br \/>\n= (x + 6)(x &#8211; 2)(x &#8211; 1)<br \/>\n= (x + 6)(x(x &#8211; 1)-2(x &#8211; 1))<br \/>\n= (x + 6)(x\u00b2 &#8211; x &#8211; 2x + 2)<br \/>\n= (x + 6)(x\u00b2 &#8211;\u00a0 3x + 2)<br \/>\n= x(x\u00b2 &#8211; 3x + 2) + 6(x\u00b2 &#8211;\u00a0 3x + 2)<br \/>\n= x\u00b3 &#8211; 3x\u00b2 + 2x + 6x\u00b2 &#8211; 18x + 12<br \/>\n= x\u00b3 + 3x\u00b2 &#8211; 16x + 12<\/p>\n<h3><a id=\"Polynomial_Equations_and_Factoring_Cumulative_Assessment\"><\/a>Polynomial Equations and Factoring Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nClassify each polynomial by the number of terms. Then order the polynomials by degree from least to greatest.<br \/>\na. -4x<sup>3<\/sup><br \/>\nb. 6y &#8211; 3y<sup>5<\/sup><br \/>\nc. c<sup>2<\/sup> + 2 + c<br \/>\nd. -10d<sup>4<\/sup> + 7d<sup>2<\/sup><br \/>\ne. -5z<sup>11<\/sup> + 8z<sup>12<\/sup><br \/>\nf. 3b<sup>6<\/sup> &#8211; 12b<sup>8<\/sup> + 4b<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"266\"><strong>polynomial<\/strong><\/td>\n<td width=\"266\"><strong>Degree<\/strong><\/td>\n<td width=\"266\"><strong>Number of terms<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"266\">-4x<sup>3<\/sup><\/td>\n<td width=\"266\">3<\/td>\n<td width=\"266\">1<\/td>\n<\/tr>\n<tr>\n<td width=\"266\">6y &#8211; 3y<sup>5<\/sup><\/td>\n<td width=\"266\">5<\/td>\n<td width=\"266\">2<\/td>\n<\/tr>\n<tr>\n<td width=\"266\">c<sup>2<\/sup> + 2 + c<\/td>\n<td width=\"266\">2<\/td>\n<td width=\"266\">3<\/td>\n<\/tr>\n<tr>\n<td width=\"266\">-10d<sup>4<\/sup> + 7d<sup>2<\/sup><\/td>\n<td width=\"266\">4<\/td>\n<td width=\"266\">2<\/td>\n<\/tr>\n<tr>\n<td width=\"266\">-5z<sup>11<\/sup> + 8z<sup>12<\/sup><\/td>\n<td width=\"266\">12<\/td>\n<td width=\"266\">2<\/td>\n<\/tr>\n<tr>\n<td width=\"266\">3b<sup>6<\/sup> &#8211; 12b<sup>8<\/sup> + 4b<sup>4<\/sup><\/td>\n<td width=\"266\">8<\/td>\n<td width=\"266\">3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Question 2.<br \/>\nWhich exponential function is increasing the fastest over the interval x = 0 to x = 2 ?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36689\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring ca 2\" width=\"565\" height=\"289\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-2.png 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-2-300x153.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\nAnswer:<br \/>\nAn exponential function j models a relationship in which the dependent variable is multiplied by 6 for every 1 unit the independent variable increases.<br \/>\nThe value of the function at 0 is 2.<br \/>\nOption D is the correct answer.<\/p>\n<p>Question 3.<br \/>\nFind all solutions of the equation x<sup>3<\/sup> + 6x<sup>2<\/sup> &#8211; 4x = 24.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36690\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring ca 3\" width=\"541\" height=\"59\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-3.png 541w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-3-300x33.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><br \/>\nAnswer:<br \/>\nx<sup>3<\/sup> + 6x<sup>2<\/sup> &#8211; 4x = 24<br \/>\nput x = -6<br \/>\n(-6)\u00b3 + 6(-6)\u00b2 &#8211; 4(-6) = 24<br \/>\n-216 + 216 + 24 = 24<br \/>\n24 = 24<br \/>\nput x = -4<br \/>\n(-4)\u00b3 + 6(-4)\u00b2 &#8211; 4(-4) = 24<br \/>\n-64 + 96 + 16 = 24<br \/>\n48 = 24<br \/>\nLHS \u2260 RHS<br \/>\nx = -2<br \/>\n(-2)\u00b3 + 6(-2)\u00b2 &#8211; 4(-2) = 24<br \/>\n-8 + 24 + 8 = 24<br \/>\n24 = 24<br \/>\nLHS = RHS<br \/>\nx = -1<br \/>\n(-1)\u00b3 + 6(-1)\u00b2 &#8211; 4(-1) = 24<br \/>\n-1 + 6 + 4 = 24<br \/>\n9 = 24<br \/>\nLHS \u2260 RHS<br \/>\nx = 2<br \/>\n(2)\u00b3 + 6(2)\u00b2 &#8211; 4(2) = 24<br \/>\n8 + 24 &#8211; 8 = 24<br \/>\n24 = 24<br \/>\nLHS = RHS<\/p>\n<p>Question 4.<br \/>\nThe table shows the distances you travel over a 6-hour period. Create an equation that models the distance traveled as a function of the number of hours.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36691\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-4.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring ca 4\" width=\"238\" height=\"190\" \/><br \/>\nAnswer:<br \/>\nm = y2 &#8211; y1\/x2 &#8211; x1<br \/>\nm = 123 &#8211; 62\/2 &#8211; 1<br \/>\n= 61<br \/>\ny &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 62 = 61(x &#8211; 1)<br \/>\ny &#8211; 62 = 61x &#8211; 61<br \/>\ny = 61x &#8211; 61 + 62<br \/>\ny = 61x + 1<\/p>\n<p>Question 5.<br \/>\nConsider the equation y = &#8211; \\(\\frac{1}{3}\\)x + 2.<br \/>\na. Graph the equation in a coordinate plane.<br \/>\nb. Does the equation represent a linear or nonlinear function?<br \/>\nc. Is the domain discrete or continuous?<br \/>\nAnswer:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-194445 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-7-Polynomial-Equations-and-Factoring-cumulative-assessement_5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring cumulative assessement_5\" width=\"686\" height=\"685\" \/><br \/>\nIt is a linear function.<br \/>\nThe domain is continuous.<\/p>\n<p>Question 6.<br \/>\nWhich expressions are equivalent to -2x + 15x<sup>2<\/sup> &#8211; 8?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36692\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-6.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring ca 6\" width=\"392\" height=\"163\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-6.png 392w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-6-300x125.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\nAnswer:<br \/>\n-2x + 15x<sup>2<\/sup> &#8211; 8<br \/>\n(5x &#8211; 4)(3x + 2) = 15x\u00b2 &#8211; 2x &#8211; 8<br \/>\n(3x + 2)(5x &#8211; 4) = 15x\u00b2 &#8211; 2x &#8211; 8<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-194446 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-6.png\" alt=\"Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-6\" width=\"392\" height=\"163\" \/><\/p>\n<p>Question 7.<br \/>\nThe graph shows the function f(x) = 2(3)<sup>x<\/sup>.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36693\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring ca 7\" width=\"197\" height=\"207\" \/><br \/>\na. Is the function increasing or decreasing for increasing values of x?<br \/>\nb. Identify any x- and y-intercepts.<br \/>\nAnswer:<br \/>\nf(x) = 2(3)<sup>x<br \/>\n<\/sup>The function is increasing.<br \/>\nThe x-intercept does not exist as it is an increasing function.<br \/>\nthe y-intercept is 2.<\/p>\n<p>Question 8.<br \/>\nWhich polynomial represents the product of 2x &#8211; 4 and x<sup>2<\/sup> + 6x &#8211; 2?<br \/>\nA. 2x<sup>3<\/sup> + 8x<sup>2<\/sup> &#8211; 4x + 8<br \/>\nB. 2x<sup>3<\/sup> + 8x<sup>2<\/sup> &#8211; 28x + 8<br \/>\nC. 2x<sup>3<\/sup> + 8<br \/>\nD. 2x<sup>3<\/sup> &#8211; 24x &#8211; 2<br \/>\nAnswer:<br \/>\n2x &#8211; 4 and x<sup>2<\/sup> + 6x &#8211; 2<br \/>\n(2x &#8211; 4)(x<sup>2<\/sup> + 6x &#8211; 2)<br \/>\n2x(x<sup>2<\/sup> + 6x &#8211; 2) &#8211; 4(x<sup>2<\/sup> + 6x &#8211; 2)<br \/>\n2x\u00b3 + 12x\u00b2 &#8211; 4x &#8211; 4x\u00b2 &#8211; 24x + 8<br \/>\n2x\u00b3 + 8x\u00b2 &#8211; 28x + 8<br \/>\nOption B is the correct answer.<\/p>\n<p>Question 9.<br \/>\nYou are playing miniature golf on the hole shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36694\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-7-Polynomial-Equations-and-Factoring-ca-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 7 Polynomial Equations and Factoring ca 9\" width=\"242\" height=\"212\" \/><br \/>\na. Write a polynomial that represents the area of the golf hole.<br \/>\nb. Write a polynomial that represents the perimeter of the golf hole.<br \/>\nc. Find the perimeter of the golf hole when the area is 216 square feet.<br \/>\nAnswer:<br \/>\nlength = 2x + 4<br \/>\nwidth = 3x<br \/>\nA = (x + 4)(3x)<br \/>\nA = 3x\u00b2 + 12x sq. ft<br \/>\nTotal area = x\u00b2 + 3x\u00b2 + 12x = 4x\u00b2 + 12x<br \/>\nP = x + 4 + x + 4 + 3x + 3x + x + x<br \/>\nP = 10x + 8 ft<br \/>\n4x\u00b2 + 12x = 216<br \/>\n4x\u00b2 + 12x &#8211; 216 = 0<br \/>\n4(x\u00b2 + 3x &#8211; 54) = 0<br \/>\nx\u00b2 + 3x &#8211; 54 = 0<br \/>\n(x + 9)(x &#8211; 6) = 0<br \/>\nx + 9 = 0 or x &#8211; 6 = 0<br \/>\nx = -9 or x = 6<br \/>\nP = 10(6) + 8<br \/>\nP = 60 + 8<br \/>\nP = 68 ft<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Download pdf Chapter 7 Polynomial Equations and Factoring Big Ideas Math Algebra 1 Answers is available here. So, all the students who are worried to solve the Big Ideas Math Book Algebra 1 Ch 7 Polynomial Equations and Factoring can get them from here. 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