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

has as a factor. When is divided by 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.