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'Root to Poly' printed from

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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?