I have a question, I think I don't understand this material very well and could use an explanation / some help.
Basically we are asked to decompose $x^5-x$ to irreducible factors over $R,F2,F5,C$
But I don't understand how the field has anything to do with it?
I would just say: $x^5-x = x(x^4-1) = x(x^2-1)(x^2+1) = x(x-1)(x+1)(x^2+1)$ and that's it, I can't factor it anymore. I don't see how fields are related.