Why do this problem?

It gives practice in manipulation of polynomials.

Possible approach

An easy lesson starter!

Key question

What is $p(x)-q(x)$?

Possible
extension

Learners can make up their own probems by writing down two
polynomials in $x$ and then eliminating $x$ between the
expressions. They might be asked to make up such a problem and
exchange problems with their partner. Then they can compare and
check results in pairs.

Possible support

Try a simpler example such as: find the formula relating $p$ and $q$ where $p=x+3$ and $q=x^2$.