In my opinion, the best way to have your query upvoted rather than downvoted is by first taking a serious look at this article. Hitting the high points of this article:
Use MathJax
Present the problem as clearly as possible. Try not to assume that MathSE reviewers will be familiar with the conventions in your class. For example, does $\log(x)$ refer to natural logarithms, logarithms base $10$, or logarithms to some other base. When in doubt, include pertinent definitions that relate to your problem.
Edit-Images
When including an image with your posting, please embed the image directly into your posting, rather than providing a link to another webpage. For help managing an image, see the Images section, at the bottom of
this article
and see also this article.
Also, please only use an image to visually illustrate a specific aspect of your problem. For example, using an image to help MathSE reviewers grasp a Geometry problem, or to present a graph of data.
Please do not use an image to present the Math inherent in the problem, such as presenting Math text from a book. That is specifically what MathJax is for. See also this article on not using an image to explain Math.
Describe the source of the problem. If it is from a book or class, what is the name of the book or class. If it is not (e.g. if it is from a contest), mention which contest. If instead, this is just an interesting problem that you thought of on your own, say so.
If the problem is from a book or class, then (assuming that this is not postgraduate work) there must have been theorems or previously solved problems or worked examples that led up to this problem. Typically, these may be regarded as the tools that you are supposed to use to attack the problem.
Describe the tools that you think might be relevant in your query. In effect you are speculating that the intent of the problem composer is that the problem is an application of the tools.
Even if this is just a problem that you thought of on your own, you might still be able to speculate as to what tools might be helpful here.
Edit
Virtually no query poster makes the effort to summarize the pertinent tools. Any mathSE query that actually does include the pertinent tools is probably going to create a positive reaction among mathSE reviewers.
Edit-Tools
I think that it is impossible for the question poster to show work unless the question poster first does work. Further, I think that it is impossible for the question poster to actually do work unless the question poster first, either consciously or subconsciously, gathers the tools that he regards as pertinent. Often, when the question poster is legitimately lost as to how to attack the problem, this often overlooked preliminary step becomes critical.
Describe your own math education - grade level - sophistication. Reviewers enjoy knowing up front what level of math to throw at the original poster.
Make a very serious effort to solve the problem on your own, and be sure to show all of your work, in excruciating detail in your query. If you tried more than one approach, show everything that you tried, in as well organized a manner as possible.
Assuming that (for example), you showed work, and reached a blockade, and need to insert pertinent question(s) in your query, try to avoid a question like "What do I do now?"
Instead, you might try a question like,
"My work has led to an answer that the back of the book says is wrong. Where is my mistake?"
or
"At this point, I suspect that I am supposed to use theorem XYZ, which is one of my tools. However, at this point in my analysis, I can't verify that the hypothesis of theorem XYZ is being met. What other analysis is needed to meet the hypothesis of theorem XYZ?"
Have your query title include at least one word in English, so that reviewers can mouse-right-click to bring up the query. At the same time, use MathJax in your query title so that the title indicates in as much detail as is reasonably possible, what you are going to ask about.
This is the type of consideration towards others that mathSE reviewers are going to appreciate.
After you format the query title, the mathSE interface will suggest mathSE queries that might have already focused on your problem. Before you post, explore any mathSE queries that you think might be relevant.
You can also use the mathSE search interface to independently search for relevant queries. One way to positively impress reviewers is by stating in your query:
I noticed the following other query {include the link}. However, although that query appears to be similar, it doesn't specifically address the question that I have because...
Or
I reviewed this other query, which does answer my question, but I don't understand the answer given by ... In his answer, he makes the following claim... Why is this claim true?
Note that this is not that unusual, because the query poster of the previous query may have had a background different from yours. The answer was intended to communicate with his level of education, not yours.
Edit
MathSE reviewers will sometimes cite a previous query as a duplicate, even though it hasn't exactly addressed your specific question. When you take the initiative to include a link + a discussion of a previous query, in your query, mathSE reviewers are going to like that.
Before you post, proofread your query. You are not only looking for typos, but also ambiguities, where it isn't crystal clear what you are asking. Try to provide such clear detail in your query that it is impossible for anyone to be unsure what you are asking.
When a mathSE reviewer encounters a high quality query, it will be like a breath of fresh air.
