x2-x-12 factor completely

Question

if the polynomial cannot be factored write prim

Answer 1

Let's take a look at the factors of 12:  12 & 1, 6  & 2, and 4 & 3.

 

Since the last term is -12, one of the factors will have to be positive and one negative.  We also need the two factors to be one apart, since the middle term is -x.

 

(x - 4)(x + 3) = x² - 4x + 3x - 12 = x² - x - 12