# Irreducible Polynomial over a Field

Please see the attached file for the fully formatted problems.

5. Find an irreducible polynomial f(x) over the field Z3 with

Z3[x]/(f(x)) = F243.

Note that 243 = 3^5 .

Please explain your reasoning and solution in as much detail as possible.

Thank You.

https://brainmass.com/math/basic-algebra/irreducible-polynomial-over-a-field-11704

#### Solution Summary

An irreducible polynomial over a given field is found. The solution is detailed and well presented.

$2.19