# 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.
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 $\mathbb{Z}_3$ .