Use the Remainder Theorem to divide 2x2 + 5x – 12 by x + 4. What is the remainder?

The Remainder Theorem tells us to use the x value of the factor and sub it in for x in our polynomial and what we get in the end is the remainder we would get if we did the synthetic division on it or long division.  P(-4)=2(-4)^2+5(-4)-12 is P(-4) = 32 - 20 - 12, and P(-4) = 0.  That means when we divide the polynomial by x + 4, we do not get a remainder and the root x = -4 is a factor of the polynomial.