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### Number and algebra

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### For younger learners

# Root to Poly

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?

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### Rudolff's Problem

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Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

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?

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?