# Irreducibility in $\mathbb{F}_3[x]$

How do we know if something is reducible/irreducible in $\mathbb{F}_3[x]$ in terms of polynomials?

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Please try accept questions when they please you. As people tend to not answer questions from people with a low accepting rate. – sxd Dec 2 '11 at 1:56
What does it mean for a nonzero nonunit element of an integral domain to be irreducible? – user5137 Dec 2 '11 at 2:03
Check this. maths.anu.edu.au/~brent/pd/BCTCS09t4.pdf – user2468 Dec 2 '11 at 2:15

We could be particularly brute force about it, and see whether $f\in\mathbb{F}_3[x]$ is irreducible by simply checking every polynomial in $\mathbb{F}_3[x]$ of degree less than $\deg(f)$ to see if it is a factor of $f$.