Find all monic irreducible polynomicals

**page929** · February 8th 2011, 08:30 AM

My question is the following:

Find all monic irreducible polynomials of degree <= 3 over Z3. Then, using the list write (x^2 - 2x + 1) as a product of irreducible polynomials.

Any help would be greatly appreciated. Thanks in advance.

**FernandoRevilla** · February 8th 2011, 10:06 AM

Hint :

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

Fernando Revilla

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