Factor x8−x in Z[x] and in Z2[x]
Here what I get is x8−x=x(x7−1)=x(x−1)(1+x+x2+⋯+x6) now what next? Help in both the cases in Z[x] and in Z2[x]
Edit: I think (1+x+x2+⋯+x6) is cyclotomic polynomial for p=7 so it is irred over Z. Now the problem remains for Z2[x]
Answer
After my edit I finally got the answer it was under my nose the polynomial 1+⋯+x6 does not have zeros at 0 and 1 so it can't be factored as a multiple of a one degree polynomial and one other as a whole.
Edit: But as Lubin mentioned in the comment 1+⋯+x6=(1+x+x3)(1+x2+x3)
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