I answered the following question and saw the asker was downvoted:

What are the elements of $\mathbb Z/3[x]$?

https://www.youtube.com/watch?v=rxc8uQJV7Kg in this video he shows the division algorithm for polynomials in $\mathbb{Z}/3[x]$. Also, what exactly is $3[x]$?

While I agree its not your run of the mill "here's my question, here's my attempt to try to solve it, here's why I can't find/understand any other relevant doc that is in the internet"

It also was a purely syntactic question, which I feel requires less explanation. The video features some text which is pretty ambiguous to someone not well experienced with the field. And the user, I'd imagine was relatively new to Abstract Algebra and was legitimately unsure how to interpret.

Do we want to discourage this type of question in the future? I feel a bit confused since to me the value of this community isn't limited to itself, but also to how much it improves the value of other external resources.

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    $\begingroup$ It seems just poorly posed without show any effort and without explaining doubts in detail. Of course it should be better to let know to the asker as to improve it math.meta.stackexchange.com/questions/9959/…. $\endgroup$ – gimusi May 7 '18 at 19:50
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    $\begingroup$ I agree that "purely syntactic" questions require less in the way of "show your work" context, but other forms of context may be important. In particular a poorly worded Question may strike you on that account as being "purely syntactical" without it being clear to the OP that their difficulty lies in a syntactic misunderstanding. If the OP can be coached somehow to expressly state their desire to use proper syntax, I'm likely to be more sympathetic. In any case there is little point in asking why anonymous votes are taken, whether down or up. $\endgroup$ – hardmath May 7 '18 at 21:33
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    $\begingroup$ Honestly, the fact that the question starts with a link to a Youtube video is problematic. $\endgroup$ – Xander Henderson May 7 '18 at 22:06
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    $\begingroup$ @XanderHenderson I've never noticed a general problem with video links. What do you think of this question? $\endgroup$ – Mark McClure May 7 '18 at 23:50
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    $\begingroup$ @MarkMcClure The question you cite is, I think, slightly superior. The asker cites the video as inspiration, then proceeds to sketch out the interesting idea from the video in a reasonably well structured (and grammatical) manner. The question at the top of this post points to the video, then says "What is this notation?" The fractal question can be answered without watching the video; in the case of the current question, it is more difficult. Not that I have any real problem with either question. :) $\endgroup$ – Xander Henderson May 8 '18 at 1:04

Reading the question it is entirely unclear what the asker knows and does not know. For instance: do they know what $\mathbb{Z}/3\mathbb{Z}$ is? If you read the comments under your answer, it would seem like they do, but nowhere does the question reflect this. Do they know what $R[x]$ means when $R$ is a ring? Do they think that $3[x]$ is an ideal? What do they know about quotient rings? Do they understand the difference between polynomials as algebraic objects vs polyomials as functions?

There's just too many questions that are impossible to answer with what little is written. Here's an example of how the question could be improved.

I'm new to abstract algebra, we've just finished covering the division algorithm for polynomials in $\mathbb Q$. I was watching this youtube video (link) which demonstrates the division algorithm for polynomials over $\mathbb{Z}/3[x]$, but I don't understand the notation.

I understand that $\mathbb{Z}/3\mathbb{Z}$ is the integers modulo $3$ but what does $3[x]$ mean? Does this have something to do with the polynomials using $x$ as a variable? Is this a quotient ring where we introduce $x$ as a variable?

Also, can someone tell me what the elements of $\mathbb{Z}/3[x]$ are?


Finally, adding more context to questions makes me more willing to put more detail in my answers. Here I might explain:

  • that $\mathbb Z/n$ is short hand for $\mathbb Z/n\mathbb Z$ and that $\mathbb Z_n$ is another notation for the same thing, and that $\mathbb Z_p$ can also denote the $p$-adics

  • that $R[x]$, where $R$ is a ring, denotes polynomials in $R$ and that $R(x)$ are rational functions and that neither are actually "functions" on $R$

Without context, not only do I feel like my time isn't appreciated well, I also don't know if I would be wasting my time explaining this. That is, if the asker already knows something, I know I don't need to explain it.

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    $\begingroup$ This will be one of my new go-to threads when "context" comes up. Brilliant answer. $\endgroup$ – quid May 7 '18 at 23:07

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