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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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? Please Help Notice that, Since we are in we have that, . 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.
OK I see what you are saying. I forgot about the Z3 [x] which makes it reducible
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