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Math Help - Finding monic irreducible polynomials.

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    Finding monic irreducible polynomials.

    13. Find all monic irreducible polynomials of degree \leq 3 over \bbold{Z}_3. The problem before this contains a hint that says to derive a way to tell "at a glance" whether or not a polynomial has a root. I'm just not seeing it, any suggestions would be appreciated. This problem comes from section 4.2 of Abstract Algebra: Third Edition by John A. Beachy and William D. Blair for those that are interested.

    Oh and also, the \bbold{Z}_3 denotes the set of integers mod n, in case you are not familiar with that notation.
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    MHF Contributor FernandoRevilla's Avatar
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    All polynomals of degree 1 are irreducible. On the other hand, a polynomial p(x)\in \mathbb{Z}_3[x] of degree 2 or 3 is reducible iff p(x) has a root in \mathbb{Z}_3 .


    Fernando Revilla
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