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.
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.
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