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Powerful Factors

Age 16 to 18
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Why do this problem?

For practice in factorising polynomials.

Key question

What is the highest power of 5 we can find using a calculator?

Can we factorise this expression to get factors involving smaller powers of 5, so that all the powers of 5 can be found using a calculator?

Howdo you know if a number is divisible by 3?

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Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

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Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Parabella

This is a beautiful result involving a parabola and parallels.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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