# Math Help - a maximal ideal

1. ## a maximal ideal

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

2. It is easy to prove that

$\mathbb{Q}[x]/(x)=\{\lambda+(x):\;\lambda\in \mathbb{Q}\}$

As a consequence,

$\mathbb{Q}[x]/(x)$ is a field.

Fernando Revilla