I'm trying to prove that $f(X)=2X^5 -10X+5$ is irreducible and the book that I'm following says that this is given by Eisenstein's Criterion. The problem is that I don't know how to use Eisenstein with a polynomial that is not monic. I thought dividing by $2$ but that gives $5/2$ that I don't know how to work with.
2026-03-28 09:43:57.1774691037
Proving $2X^5 -10X+5$ is irreducible.
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Recall that for using Eisenstein's criteria you just need to find a prime $p$ which divides all the coefficients apart from the leading coefficient of the polynomial and $p^2$ doesn't divide the constant term...there is no restriction on the polynomial being monic or not. As such, for your problem $p=5$ does the job.