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'Polynomial Relations' printed from https://nrich.maths.org/
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 $q=x^2$.