[SOLVED] Algebraic Division

Normal algebraic division using remainder or factor theorem is usually fine however this exam question asks to find values in a different way:

The polynomial

$\displaystyle f(x) = px^3 - x^2 + qx - 6$

has $\displaystyle (x - 3)$ as a factor. When $\displaystyle f(x)$ is divided by $\displaystyle (x - 2) $ the remainder is -20.

Show that p = 2 and find the value of q.

I can find these values easily by division however the question is worth 6 marks and requires a different approach.

How would you work this question out with that in mind?

Thanks if you can help.