13. Find all monic irreducible polynomials of degree $\displaystyle \leq$ 3 over $\displaystyle \bbold{Z}_3$. 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 ofAbstract Algebra: Third Editionby John A. Beachy and William D. Blair for those that are interested.

Oh and also, the $\displaystyle \bbold{Z}_3$ denotes the set of integers mod n, in case you are not familiar with that notation.