My question is the following:

Find all monic irreducible polynomials of degree <= 3 overZ3. Then, using the list write (x^2 - 2x + 1) as a product of irreducible polynomials.

Any help would be greatly appreciated. Thanks in advance.

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- Feb 8th 2011, 08:30 AMpage929Find all monic irreducible polynomicals
My question is the following:

Find all monic irreducible polynomials of degree <= 3 over**Z**3. Then, using the list write (x^2 - 2x + 1) as a product of irreducible polynomials.

Any help would be greatly appreciated. Thanks in advance. - Feb 8th 2011, 10:06 AMFernandoRevilla
:__Hint__

All polynomals of degree $\displaystyle 1$ are irreducible. On the other hand, a polynomial $\displaystyle p(x)\in \mathbb{Z}_3[x]$ of degree $\displaystyle 2$ or $\displaystyle 3$ is reducible iff $\displaystyle p(x)$ has a root in $\displaystyle \mathbb{Z}_3$ .

Fernando Revilla