Question

Is the given linear expression a factor if the polynomial?

f(x) = 2x^3 + x^2 - 5x + 2; x + 2​

Answer 1

Yes.

Explanation:

Given: f(x) = 2x^3 + x^2 - 5x + 2; x + 2​

If x + 2 is a factor of f(x), then , by the Factor Theorem, f(-2) = 0.

So we check if this is so:

f(-2) = 2(-2)^3 + (-2)^2 - 5(-2) + 2

= -16 + 4 + 10 + 2

= -16 + 16 = 0.

So Yes x + 2 is a factor.