Question

Use the Factor Theorem to determine whether x+2 is a factor of P(x)= -x^4 - 2x^3 + 6x^2 - 24.
Specifically, evaluate at the proper value, and then determine whether x+2 is a factor.

P(?)=?

Answer 1

If for any x = a
f(a) = 0 , then x - a is a factor

so....
P(x)= -x^4 - 2x^3 + 6x^2 - 24
P(-2) = -(-2)^4 - 2(-2)^3 + 6(-2)^2 - 24
= -16 + 16 + 24 - 24 = 0

therefore (x+2) is a factor