I have following two field and would like to prove those two are isomorphism as a field.
$F_1 = \Bbb Z_3[x] /( x^3+x^2+2)$
$F_2 = \Bbb Z_3[x]/(x^3 + 2x+2)$
Then I might have to prove 1) addition and multiplication are preserved well through a specific function between $F_1$ and $F_2$ also with it well transfer identity's of one field.
However, to prove that well-preservation of operation, how could I normally think the representative element of quotient field of polynomial?
Any idea how to get those?