Use the Factor Theorem to determine whether x+2 is a factor of P(x)=2x^4+x^3-4x^2-8

Question

Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.

P(?)=?

Answer 1

If P(c) = 0, then x - c is a factor of P(x). Otherwise, x - c is not a factor of P(x).

Now, x + 2 = x - (-2), so we must investigate P(-2).

P(-2) = 32 - 8 - 16 - 8 = 0

Therefore, x - (-2) (i.e., x + 2) is a factor of P(x).