I have looked at many websites and forums and none were really that helpful. So my question is, is there an easy way such as a formula or pattern that you can create an irreducible polynomial over $GF(2)$ or $GF(3)$. I know that $x^2+x+1$ is an irreducible polynomial over $GF(2)$. But
How can you tell when the polynomial is longer such as $x^5 +x^3 + x^2 +1$ if it is an irreducible polynomial over $GF(2)$ or $GF(3)$.
I get what an irreducible polynomial is but I want an easy way to verify.