2002 AMC 10P Problem 11

Let P(x)=kx^3 + 2k^2x^2+k^3. Find the sum of all real numbers k for which x-2 is a factor of P(x).

\text{(A) }-8 \qquad \text{(B) }-4 \qquad \text{(C) }0 \qquad \text{(D) }5 \qquad \text{(E) }8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.