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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 $(x-p)(x-q)$

Can someone PLEASE help me with this question? I have no clue how to start this question. Thanks guys in advance.

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

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