1. ## Irreducible????

Question:
Determine if x^4 + x^2 + 1 is ireducible in Z3[x]. Factorize it if you can

I think x^4 + x^2 + 1 can be factored as
(x^2 +2)(x^2 +2)

which would make it Irreducible but not sure?

2. Originally Posted by mathlg
Question:
Determine if x^4 + x^2 + 1 is ireducible in Z3[x]. Factorize it if you can

I think x^4 + x^2 + 1 can be factored as
(x^2 +2)(x^2 +2)

which would make it Irreducible but not sure?

$(x^2+2)(x^2+2)=x^4+4x^2+4$
Since we are in $\mathbb{Z}_3[x]$ we have that,
$x^4+x^2+1$.