in general: look for what the terms have in common. for example, take the binomial 2x² - 4x. you would be able to factor out a "2" because of the coefficients, and both terms have an "x" -- you can take that out too. that makes your GCF 2x. technically, what you're doing with factoring is dividing the terms by your GCF--2x² divided by 2x leaves you with x, and 4x divided by 2x leaves you with two. that's how you end up with (x - 2) in your binomial. your result looks like this: 2x(x - 2).
if you have any specific binomials you need help with, feel free to send me a message or comment on this and i'll see if i can help. if you're just asking in general, then just remember to look for what the terms have in common, then take it out.
