I need to show the following problem
if $K$ is any finite extension of $\mathbb{Q}$, then there exists an integer $n$ and a maximal ideal $M$ of the $n$ variable polynomial ring $\mathbb{Q}[x_1,\cdots,x_n]$ such that
$K \simeq \mathbb{Q}[x_1,\cdots,x_n]/M $.
I think since $K$ is a finite extension of $\mathbb{Q}$, then there is a basis $\{\alpha_1, \cdots,\alpha_n\}$ for $K$ as a vector space over $\mathbb{Q}$, for some $n$. Moreover, $\alpha_i$ is algebraic over $\mathbb{Q}$ for each $i$.
I am not quite sure how to prove the existence of the maximal ideal.