I had to do some homework problems involving the polynomial ring $R=\mathbb{Z}+x\,\mathbb{Q}[x]\subset\mathbb{Q}[x]$. This is an integral domain but not a UFD. Further, $x$ is not prime in $R$.
One of the problems was to describe to $R/(x)$.
Since $x$ is not a prime element, we know $(x)$ is not a prime ideal. So at the very least, $R/(x)$ is not an integral domain.... but what else can I say? This is perhaps something I should not admit, but problems of this form have always befuddled me. I know there's not any one "answer" they're looking for, but I never quite know what to say.
Anyway, this homework has been submitted already, so I am not including a homework tag. I'm just curious how you all would describe this particular quotient.