All polynomals of degree are irreducible. On the other hand, a polynomial of degree or is reducible iff has a root in .
13. Find all monic irreducible polynomials of degree 3 over . 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 denotes the set of integers mod n, in case you are not familiar with that notation.