Prove that for any postive integer $n$, the polynomial $$(X^2+2)^n+5(X^{2n-1}+10X^n+5)$$ is irreducible in $\mathbb Z[X]$.
I have try use Eisenstein's criterion and can't it
2026-04-04 10:19:02.1775297942
The polynomial $(X^2+2)^n+5(X^{2n-1}+10X^n+5)$ is irreducible in $\mathbb Z[X]$
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This is an immediate application of the Schönemann's Irreducibility Criterion. It also follows by reducing modulo $5$ twice.