We consider the algebraic expression 4x+8. This expression is already simplified but notice that 4 and 8 have a common factor. In fact the HCF of 4 and 8 is 4.

Now, 8 = 4 x 2 and 4 = 4 x 1

So, 4x + 8 = 4 x 1x – 4 x 2

= 4(x + 2)

Notice that the HCF has been taken out of the bracket and written at the front. The terms inside are found by considering what you need to multiply by 4 to get 4x and 8.

As we explained in the definition above this process of writing an algebraic expression using brackets in this way is known as factorization. The expression 4x+8 has been factorized to give 4(x+2).