Question

How do you use the factor theorem to determine whether x+3 is a factor of `-4x^3 + 5x^2 + 8`?

Answer 1

You evaluate this polynomial at `x = -3`.

Explanation:

Let `P(X) = -4X^3 + 5X^2 + 8`. If `X+3` is a factor of `P`, then `P(-3) = 0`. Let's evaluate `P` at `3`.

`P(-3) = -4*(-3)^3 + 5*3^2 + 8 = 108 + 45 + 8 != 0` so `X+3` is not a factor of `P`.