Prove that the ideal (x) in Q[x] is maximal. (Q[x] is the set of all polynomials with rational coefficients
any help would be appreciated
It is easy to prove that
$\displaystyle \mathbb{Q}[x]/(x)=\{\lambda+(x):\;\lambda\in \mathbb{Q}\}$
As a consequence,
$\displaystyle \mathbb{Q}[x]/(x)$ is a field.
Fernando Revilla