Calculating value of Q,when remainder is given. 3rd degree polynomial

Question

If $f(X) = 2x^3 + 4qx^2 - 3q^2x -2$ is divided by $x-q$ the remainder is $10$, then calculate the value of $q$.

Tried factoring the polynomial.

Obtain quotient by means of long division.

I am truly missing something here. Please help.

Answer 1

Asserting that the remainder of the division of $f(x)$ by $x-q$ is $10$ is the same thing as asserting that $f(q)=10$. So, solve the equation $f(q)=10$.

Answer 2

HINT:

\begin{equation}\begin{aligned} f(x) &= 2x^3+4qx^2-3q^2x-2 \\ &= 2x^3-2qx^2+6qx^2-6q^2x+3q^2x-3q^3+3q^3-2 \\ &= 2x^2(x-q)+6qx(x-q)+3q^2(x-q)+3q^3-2 \\ &= (x-q)(2x^2+6qz+3q^2)+3q^3-2 \\ \end{aligned}\end{equation}