Polynomial Functions, fundamental question.

When a polynomial is divided by $x-p$, the remainder is $p^3$ . When the polynomial is divided by $x-q$, the remainder is $q^3$ . Find the remainder when the polynomial is divided by $(x-p)(x-q)$

Hint: The remainder is a polynomial of degree $1$, say $r(x)=ax+b$. What can you say about $r(p)$ and $r(q)$?