Which binomial is a factor of the polynomial? 2x2 + 13x - 7

a) (x - 2)
b) (x - 7)
c) (x + 7)
d) (x + 1)

With expressions like these, the first step is to factor the first term and the last term. The first term can be factored 2 ways: 2x • x, or -2x • -x. We'll have to insert both into the brackets to see which ones work. For now, let's try the positive.

(2x \ ?) (x \ ?)

Now let's factor the last term. We know it could be 7 • 1, or 3 • 4. One of them just has to be a negative. Let's put in 7 and -1

(2x - 1) (x + 7)

Now we do the math on the outers and the inners.

7 • 2x = 14x
-1 • x = -1x

14x - 1x = 13x.

Now we know that the entire factoring of the expression is:

(2x - 1) (x + 7)

Which answer choice has one of these?