Via a question I took a look at the polynomials tag and found that the tag wiki says this:
Polynomials are expressions like $15x^3 - 14x^2 + 8$. Questions tagged with this concern common operations on polynomials, like adding, multiplying, polynomial long division, factoring and solving for roots.
This tag often goes along with the algebra-precalculus tag. (This line is only shown in tag wiki, the rest appears in the excerpt.)
Looking only at the excerpt I considered editing it, since it suggests that polynomials only exist in $\mathbb R(x)$. But then I saw the tag info page (the extra line), which seems to suggest that polynomials and algebra-precalculus are closely related. In that case the tag excerpt wouldn't need to be altered, since for many people with questions at a precalculus level (and sometimes even at a slightly higher level) polynomials only do exist in $\mathbb R(x)$.
Looking at the kinds of questions with this tag I found that they vary quite a bit in level and subject. Furthermore, a lot of time the tag is accompanied by other (IMHO) way more useful tags. For instance: partial-fractions, irreducible-polynomials, roots, factoring, splitting-field and as suggested, often with algebra-precalculus.
So that led to my question: What should the polynomials tag be used for?
If it is indeed intended to be used under such a wide variety of questions, then I believe the tag wiki should be changed to say so.
If it is not intended to be used under all these questions then I believe the tag wiki should also say so.
Personally I don't care to much for the polynomials tag, because I feel that there are much more useful tags available. In any case I believe that currently the suggestion that polynomials and algebra-precalculus often go together is misleading. Especially since this is not the case for a great number of question carrying this tag.