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.

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