I'm supposed to factor 4x^2 – 8x... it's a multiple choice question and I can't decide between three of the answers... my first thought was 2x(2x-4) but the other choices are x(4x-8) or 4x(x-2)... the only other answer choice is 4(x^2-2)... I thought I knew what I was doing but I guess not... and the example in the book isn't helping... could someone please tell me how to solve this

Just factor out the smallest of each. You have an x and an x^2, a 4 and an 8. Factor out the 4 and x.

write out the factors.

4x^2 -8x
(2*2)(x*x)-(2*2*2*x)

Here we see two terms, the factors these terms have in common are: 2 factors of 2, and 1 factor of x

(2*2)(x*x)-(2*2*2)(x)

When we pull these factors out, we essentially divide the two terms by those factors!

[2*2*x](x-2)

Forgot to add, of course you would simplify the terms to:

4x(x-2)