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

The factor theorem states that if P(c) = 0, then x - c is a factor and subsequentially, c is a zero. In this case, c = -2 because x - (-2) = x + 2.

P(-2)=2(-2)^4+(-2)^3-4(-2)^2-8

= 2 (16) + (-8) - 4(4) - 8

= 32 - 8 - 16 - 8 = 0

Therefore, x + 2 IS a factor, and -2 IS a zero.