Factorization is writing an expression as a product of factors. A factor is a number that divides a number or expression without a remainder.

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)

ax^{2}+bx+c and 6x^{2}+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.

Factors :

1 , 36

2, 18

3, 12

4, 9

-4 and 9 are factors with product -36 and sum = 9 - 4 =+5

Write the factors with x

6x^{2}+9x-4x-6.

H.C.F of 6x^{2}+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.

6x^{2}+5x-6 = (2x+3)(3x-2)