[Math] Find k so that polynomial division has remainder 0

Question

Find $k$ so that $x^3-kx^2+3x+7k$ has remainder $0$ when divided by $x+2$.

How do I approach this problem? I know how to do polynomial long division and synthetic division, but I don't know how to apply it in this equation.

Answer 1

Hint:

Let $F(x)=x^3-kx^2+3x+7k$. Then $F(-2)=0$