Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity.
As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots.
The Attempt at a Solution
So, let ω = e2πi/5. I can therefore find all the 5th roots of unity:
ω1 = e2πi/5
ω2 = ω2 = e4πi/5
ω3 = ω3 = e6πi/5
ω4 = ω4 = e8πi/5
ω5 = ω5 = e5πi/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?