Refering to this question suppose I have $l(x):=x^3+x+1$ and $m(x):=x^3+x^2+1$. Then prove there is an isomorphism between $\mathbb{F}_3 [x]/l(x)$ and $\mathbb{F}_3[x]/m(x)$
I can say that elements for both the fields are same.
$$x^3+x+1= 0,\quad 1 x,\quad x+1,\quad x^2,\quad x^2+1,\quad x^2+x,\quad x^2+x+1$$
If you already know that both are fields then all you have to do is count their order, because finite fields are uniquely determined up to isomorphism by the number of elements they contain.