## Use Eisenstein’s criterion to show that a given polynomial is irreducible

Use Eisenstein’s criterion to prove that $p(x) = x^4 - 2x^3 + 6x - 3$ is irreducible over $\mathbb{Q}$.

Evidently $p(x+1) = x^4 + 6x^3 + 12x^2 + 16x + 6$ is Eisenstein at 2, and thus is irreducible. So $p(x)$ is irreducible.