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## 'Root to Poly' printed from http://nrich.maths.org/

Why do this problem?

It gives learners experience of algebraic manipulation of
polynomials and working with surds. It is based on the fact that if
you know one root of a polynomial then you know one of its
factors.

Possible approach

This can be used as a lesson starter.

Key questions

We are looking for a polynomial in $x$, do you know any values of
$x$ that satisfy the polynomial?

If you have an expression involving surds what can you try in order
to get rid of the square roots?