If you are trying to figure out ways on factorizing algebraic expressions of the form ax2 + bx + c, a ≠ 1 then this is the right place. We have covered everything on how to factorize the expression of the form ax2 + bx + c, a ≠ 1 along with detailed steps. Employing this identity in your algebraic expression factorization makes it much simple for you. Refer to the solved examples on factorizing expressions put in the form of ax2 + bx + c and try to solve the problems on your own.
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How to Factorize Expressions of the form ax2 + bx + c, a ≠ 1?
Go through the simple steps mentioned below to factorize the expressions in the form of ax2 + bx + c, a ≠ 1. They are along the lines
- Firstly multiply the constant term and coefficient of x2, i.e. ac
- Split ac into two factors p,q where p+q=b
- Pair one of them like px with ax2 and the other one qx with c and factorize the expression.
Examples on Factorizing Expressions of the form ax2 + bx + c, a ≠ 1
Example 1.
Factorize 3m2 + 6m – 24?
Solution:
Given Expression = 3m2 + 6m – 24
3*-24 =72, 12-6 =6
= 3m2 +12m -6m- 24
=3m(m+4)-6(m+4)
= (3m-6)(m+4)
Example 2.
Factorize 5x2 + 12x + 15?
Solution:
Given Expression = 5x2 + 12x + 15
5*15=75, 15-3=12
= x2 + 7x +5x+ 35
= x(x+7)+5(x+7)
=(x+7)(x+5)
Example 3.
Factorize 30x2 + 103xy – 7y2
Solution:
Given Expression = 30x2 + 103xy – 7y2
30*7=210, 105-2=103
= 30x2 + 105xy-2xy – 7y2
= 15x(x+7y)-2y(x+7y)
= (15x-2y)(x+7y)
Example 4.
Factorize 10a2 + 17a + 3?
Solution:
Given Expression = 10a2 + 17a + 3
10*3 =30 15+2 =17
= 10a2 + 15a +2a+ 3
= 5a(2a+3)+1(2a+3)
=(5a+1)(2a+3)
Example 5.
Factorize 2x2 – x – 6?
Solution:
Given Expression = 2x2 – x – 6
2*3=6 4-3=-1
=2x2+4x-3x-6
=2x(x+2)-3(x+2)
=(2x-3)(x+2)
Example 6.
Factorize 8b2 – 21b + 10?
Solution:
Given Expression = 8b2 – 21b + 10
8*10=80,-16-5=-21
= 8b2–16b-5b+10
= 8b(b-2)-5(b-2)
=(8b-5)(b-2)