Factorization is writing an expression as a product of factors. A factor is a number that divides a number or expression without a remainder.
To factorize linear expressions:
Take the expression 4x + 32.
The highest common factor (H.C.F) of 4x and 32 is 4 so the expression can be written as a product of 4.
- Write 4 outside the brackets. Now find the expression inside the bracket.
4 ( x + _ )
- The number outside the bracket is multiplied with all terms inside the bracket.
4 * x = 4x and 4* 8 =2 so x + 8 is the expression inside the bracket.
4( x + 8)
Take the expression 4x2 + 32x.
The H.C.F is 4x.
4x * x = 4x2
4x * 8 = 32
4x ( x + 8)
To factorize quadratic expressions ax2+bx+c:
Take the expression 6x2+5x-6.
ax2+bx+c and 6x2+5x-6.
a = 6, b = 5, c = -6
Multiple a and c
a * c = 6 * 6 = -36
Write the factors of -36 and choose factors with product -36 and sum b = 5. You can change the signs of the factors.
1 , 36
-4 and 9 are factors with product -36 and sum = 9 - 4 =+5
Write the factors with x
H.C.F of 6x2+9x is 3x and H.C.F of -4x-6 is -2.
3x (2x +3) -2 (2x+3)
2x+ 3 is a common factor and 3x-2 is another factor.
6x2+5x-6 = (2x+3)(3x-2)