Proposition. A polynomial of degree 2 or 3 over a field F is reducible iff it has a root in F.(adsbygoogle = window.adsbygoogle || []).push({});

Tell me if I'm on the right track... I see that x^4 + 3x^2 + 2 is reducible (x^2+1)(x^2+2) but has no roots in Q.

This serves as a counterexample to the proposition if states for polynomial up to degree 4?

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# Irreducibles of small degree

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