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?

Please Help

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- May 7th 2006, 09:00 AMmathlgIrreducible????
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?

Please Help - May 7th 2006, 09:03 AMThePerfectHackerQuote:

Originally Posted by**mathlg**

$\displaystyle (x^2+2)(x^2+2)=x^4+4x^2+4$

Since we are in $\displaystyle \mathbb{Z}_3[x]$ we have that,

$\displaystyle x^4+x^2+1$.

Which means it is*reducible*.

Irreducible over a Field means a polynomial CANNOT be factored into non-constant polynomials as elements of that field. Which is not true here. - May 7th 2006, 09:12 AMmathlg
OK I see what you are saying. I forgot about the Z3 [x] which makes it reducible