Thread: 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?

Please Help

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