A polynomial function, in this context, means a function that is/can be expressed as a sum of powers (usually restricted to a finite number of addends) of its input variables with appropriate prefactors. For example,
f(x) = 1
exp(x) = 1 + x + 1/2 x² + 1/6 x³ + …
Furthermore, you didn’t only get downvoted for misinterpreting polynomial, but also for the strange mixing of theoretical CS, which is concerned with the complexity of algorithms at hand, and real-world effects such as slowdowns due to other programs multitasking, CPU caches etc. etc. which are rarely taken into account when deciding whether a given algorithm is remotely feasible to implement (runs in time, say, n^10 or faster) or just too slow.
So a Polynomial doesn't need be many of them, it can be just one of them. The poly in the name threw me off I admit. I would have assumed that was a mononomial for just one and two of them are a binomial but apparently polynomial is used instead even for only one or two? I hope you understand my confusion there. Thank you for clearing that up.
In science in general, including computer science, "theoretical" doesn't mean fringe or unexplored, it means foundational and abstract. CS theory uses the word "theory" in the same sense as music theory. CS theory deals with well-defined, rigorous analysis of computation in abstract or mathematical terms.
I would have assumed that was a mononomial for just one and two of them are a binomial but apparently polynomial is used instead even for only one or two?
A two-termed polynomial is also called a binomial. "Binomial" and "monomial" are special cases of the more general term "polynomial".
The relevant point is that it usually doesn’t matter whether you have one, five or 500 terms in a polynomial, as the largest one will certainly dominate for sufficiently large input sizes and all terms in a polynomial essentially behave the same way (being differentiable, having no poles etc.).
 The only thing wrong with homosexuality is smashing a Greek prefix onto a Latin root.
 Latin: uno-, bi-, pauc-, multi-, Greek: mono-, di-, oligo-, poly-
 cf. http://www.wolframalpha.com/input/?i=x%5E20%3B+x%5E20%2Bx%5E...