Question: Let $M$ be a maximal ideal in the polynomial ring $\Bbb C[x]$. Prove that there is some $a \in \Bbb C$ such that $M$ is the ideal generated by $x-a$

This question I have no idea how to prove, hope somebody help me. Thanks

Answer: 
**Hint:** $\mathbb C[x]$ is a principal ideal domain. Apply the fundamental theorem of algebra.
Another hint: What is the residue field $\mathbb C[x]/M$? What is the image of $x$ there?