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Is this true?

Irreducible over irreducible mod every prime

No — it is false.

The counterexample

This one comes with the Notes pack.

See pricing

85 counterexamples are free — including most of the ones Part C leans on hardest.

The kind of mistake this is

Base field or ring

The answer changes with the field or ring you are working over.

Drill statements like this
polynomialsfields

Others that fail the same way

From Rings and Fields › Polynomial rings and irreducibility tests

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