how do i factor

Question

x(x-8)+(x-8)

Answer 1

x(x - 8) + (x - 8)

First we need to get rid of the brackets to get the equation in the normal form:

x^2 - 8x + x - 8

x^2 - 7x - 8

 

Now we need to think about factors of 8 that would work :

8 = 8x1 = 2x4

 

In this case, after considering these factors, we can see that -8 and 1 are the only solutions that will give us -7. So,

x(x - 8) + (x - 8) = (x - 8)(x + 1)

 

You can check that this is the answer by multiplying out the brackets:

(x - 8)(x + 1) = x^2 + x  - 8x - 8 = x^2 - 7x - 8