# What questions should the (polynomials) tag be for?

Via a question I took a look at the 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 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 and 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: , , , , and as suggested, often with .

So that led to my question: What should the 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 tag, because I feel that there are much more useful tags available. In any case I believe that currently the suggestion that and often go together is misleading. Especially since this is not the case for a great number of question carrying this tag.

• Polynomials in $\Bbb R(x)$? So like $\frac{f_0(x)}{g_0(x)}+\frac{f_1(x)}{g_1(x)}X+\cdots + \frac{f_n(x)}{g_n(x)}X^n$? :P – GPerez Jun 4 '15 at 17:11
• @GPerez: No, that's a polynomial over $\mathbb R(x)$. – hmakholm left over Monica Jun 5 '15 at 16:53
• @HenningMakholm Aah, so you mean $a_0 + a_1 \Bbb R(x) + a_2 \Bbb R(x)^2 + \cdots + a_n\Bbb R(x)^n$ (I'm sorry, I had to). It was all a joke to begin with anyways. – GPerez Jun 5 '15 at 16:57

The metric I like to use when considering tag quality is searchability: does it seem feasible that someone might want to use the tag as a filter when looking for a certain type of question?

In this case, I see it being used most often as a secondary filter. For example, I could imagine someone using the tag while seeking precalculus questions involving polynomials, or probability questions involving polynomials, or recreational mathematics questions involving polynomials, etc. It is not as easy to imagine someone looking through questions about polynomials in general, since, as you point out, the scope would be quite large.

In a way, I suppose this usage is similar to a meta-tag, but I would not go so far to say that it must be used as such. Here are a few topics I could see being tagged only with :

• Questions about properties of polynomials in general, like this one.

• Particular families of polynomials. Lagrange, Chebyshev, etc.

Perhaps this list could be extended and added to the tag wiki.

• I will just point out that some special classes might have a separate tag. There are tags (chebyshev-polynomials) and (lagrange-interpolation), for example. – Martin Sleziak Jun 6 '15 at 9:23
• That would still mean that the tag wiki should be elaborated/generalized to clarify that it can be used under all sorts of questions. – gebruiker Jun 6 '15 at 15:01
• I tagged a Schubert calculus question with polynomials. It was about Schubert polynomials! – Matt Samuel Oct 16 '15 at 4:15