Consider the polynomial $\displaystyle p(x)=x^6-1$.

(a) Find all monic irreducible factors of $\displaystyle p(x)$ over $\displaystyle Q$.

(b) Find all monic irreducible factors of $\displaystyle p(x)$ over $\displaystyle R$.

(c) Find all monic irreducible factors of $\displaystyle p(x)$ over $\displaystyle C$.

I'm really not sure what to do, I know that $\displaystyle x^6 - 1 = (x^3)^2 - 1 = (x^3 - 1)(x^3 + 1) $, so the the roots of p(x) are ±1 & (x+1) & (x-1) are two linear factors. Anyway the first question here asks for monic (degree 1) irreducible (so that it cannot be factorized as P(x)=a(x)b(x) where $\displaystyle a(x), b(x) \in Q$) factors of p(x) over Q (rationals). Can anyone show me the method for solving one of them, so that I'll be able to try solving the rest of it on my own. Thanks.