Question

Factor completely. x^2−3x−40

Answer 1

This expression is a generic quadratic expression, so the first thing we need to look at is the last term (-40). Is it negative or positive? What are the factors of it? If the last term is negative, we know that one binomial is a subtraction while the other binomial is an addition. You may be asking, "an addition or subtraction of WHAT?" A binomial factored out of a quadratic expression would look something like this: (x + ____). The blank would equal a factor of the last term. In this case, a pair of factors that would fit is 8 and 5. 
8x5 = 40 and -8 + 5 = -3.

Plug it into the binomial example I provided above and....
(x - 8)(x+5)=40

Voila! You have your factored quadratic expression, hope this helps!