Is $\frac{x^2+x}{x+1}$ a polynomial?
Fist question can be: on which field/ring or etc? In basic, let's take over $\mathbb R$.
Actually, it is $x$ if $x \ne -1$.
Can we say again it is a polynomial, or a near-polynomial or what?
Can we say it is a polynomial over $\mathbb R - \{-1\}$? But there is structure here for $\mathbb R-\{-1\}$.
This question can be academically, not sure, but I want to ask it in the level of primary school, then academically.