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## Homework Statement

Decompose x

^{5}- 1 into the product of 3 polynomials with real coefficients, using roots of unity.

## Homework Equations

As far as I know, for x

^{n}= 1 for all n ∈ ℤ, there exist n distinct roots.

## The Attempt at a Solution

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So, let ω = e

^{2πi/5}. I can therefore find all the 5th roots of unity:

ω

_{1}= e

^{2πi/5}

ω

_{2}= ω

^{2}= e

^{4πi/5}

ω

_{3}= ω

^{3}= e

^{6πi/5}

ω

_{4}= ω

^{4}= e

^{8πi/5}

ω

_{5}= ω

^{5}= e

^{5πi/5}= 1

As far as I can get all the roots, I still don't quite understand how to decompose it into a product of 3 polynomials... What does it mean?