Show that this polynomial is irreducible over Q

Question

I have to show that the polynomial $1+x^p+x^{2p}+...x^{p^2-p}$ where p is a prime is irreducible over rationals. I am only looking for a hint. How should I go about this?

Answer 1

Here is a possible approach:

First note that your polynomial can be written as a finite geometric series.

Then do the variable substitution $x=y+1$ and something with Eisenstein.