The bookUnit 2 · Rings and Fields46 / 83

Polynomial rings and irreducibility tests

Why this is asked: Pick the right test: rational root, Eisenstein (possibly after a shift), or reduction mod p. Irreducible over ℚ does not mean irreducible mod every p.

Irreducibility tests

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Irreducibility tests, in the order worth trying theminteractive

Rational roots, Eisenstein, reduction mod p — and the quartic that factors despite having no real roots.

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Open this in the full syllabus view · Unit 2