1. The problem statement, all variables and given/known data Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity. 2. Relevant equations As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots. 3. 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?