Is there standard notation for an arbitrary polynomial of degree $k$?

Question

I was wondering whether there is standard notation for a polynomial of a certain degree, say, $k$. That is, I want to be able to write $<standard \text{ } notation> $ instead of "..., where $p(x)$ is a polynomial of degree $k$."

Does such a thing exist? For example, would $p^k(x)$ do the trick? I don't really see it as self-evident that it would, but there might be better notation out there.

Answer 1

I would write

$p\in\Bbb F[x],\ \deg(p)=k\,$.

Answer 2

How about p(x) = $\sum_{i=0}^k x^i a_i$? Maybe not what you're looking for, but the shorter than what you have already :)

Answer 3

Polynomials (of degree $n$) are almost always written as $$a_0+a_1x+\cdots+a_nx^n$$ or more compactly as $$\sum_{k=0}^n a_kx^k.$$