Show that the polynomial $P = x^8-6x^3+ 2x^2+2$ is irreductible in $\mathbb{Q}[x]$.
Is is possible to use Eisenstein's criteria? Otherwise, is anyone could help me to solve it?
2026-04-06 23:23:37.1775517817
Show that the polynomial $P = x^8-6x^3+ 2x^2+2$ is irreductible in $\mathbb{Q}[x]$
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Recall what Eisenstein's criterion says. If you can find a prime, p, that divides all the coefficients except the leading one. And if p^2 does not divide the constant term then that polynomial is irreducible.