factorization in Z_3

Factor x^9-x and x^{27}-x in Z_3. Prove that your factorization are
irreducible.

I've really have no idea about this.
For the first one, we need to factorize x^4+1 in Z_3.
How to do that?

And for the second one, we have to factorize a polynomial of degree 12!

Can anyone give some hints?

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