Let $F$ be a field and $f(x) = x - 1$ and $g(x) = x^2 - 1$.
1) Show that $F[x]/(f(x)) \cong F$
2) Is ideal $(g(x))$ maximal? Explain your answer.
** I have a feeling that this uses the first isomorphism for rings but I can't relate the elements of the question two the elements in the isomorphism theorem, maybe there is an other way of doing this?**