Counterexample

Is this true?

A degree-4 polynomial with no rational roots is irreducible over $\mathbb{Q}$

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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

Keep practicing

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

See real exam options built on this mistake Drill statements like this

Go deeper· Explained in full in Irreducibility tests· Asked in CSIR NET June 2025· From Rings and Fields › Polynomial rings and irreducibility tests

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