Showing irreducibility of a polynomial.

Question

How would you go about showing that $p(x)=\frac{x^5-1}{x-1}=x^4+x^3+x^2+x+1$ is irreducible over $\mathbb{Q}$. I'm having trouble seeing how one can show whether this kind of polynomials are irreducible or not

Thanks for your help.

Try showing $p(x+1)$ is irreducible using Eisenstein's criterion. https://en.wikipedia.org/wiki/Eisenstein%27s_criterion — Anurag A, Aug 07 '15 at 17:28

score 1 · Answer 1 · answered Aug 07 '15 at 17:32

1

Hint: Calculate $p(x+1)$ and note that $p(x)$ is irreducible iff $p(x+1)$ is

You may be interested in further reading about cyclotomic polynomials

answered Aug 07 '15 at 17:32

Belgi

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Showing irreducibility of a polynomial.

1 Answers1