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I am writing some math homework in LaTex and I would like to format somehow like this:

10.2) Question Statement

My Answer

Meaning, I would like the question statement stand out, either in a colored box like above, or in some other way. Is this possible? Thank you.

EDIT: Here is an example of how I would like to to look like:

10.2) Let $R$ be an integral domain. Show that if $R[x]$ is a principal ideal domain, then $R$ is a field.

Proof: The map $varphi : R[x] to R$ defined by $varphi: p(x) mapsto p(0)$ is a surjective homomorphism with kerned $(x)$. By the first isomorphism theorem, we have $R[x]/(x) cong R$. Furthermore, $(x)$ is a maximal ideal, is a prime ideal, and because $R[x]$ is a principal ideal domain, $(x)$ is maximal. Therefore $R[x]/(x)$ is a field, so $R$ is a field as well.

As others have pointed out, there are a massive range of options for doing boxed and colored text. Here's just one example. Whichever you use, you probably want to set it up as a personally defined environment: that way you can easily change the precise implementation without having to alter your document in more than one place. If you learn anything from this, learn that!

documentclass[12pt]{article}

usepackage{tcolorbox}% Here's the package we will use. Many options for sure.



newenvironment{question}[1]% We set up an environment which takes one mandatory argument: the question number.

{begin{tcolorbox}[title=#1]}% Its start is to begin a tcolorbox with our question-number as the title

{end{tcolorbox}}% And its end is just to end tcolorbox



tcbset{colback=orange!20!white,colframe=orange!75,fonttitle=sffamilybfseries}% Fiddle with colors, fonts etc here



begin{document}

begin{question}{10.2}

    Let (R) be an integral domain. Show that if (R[x]) is a principal ideal domain, then (R) is a field.

  end{question}

Proof: The map (varphi : R[x] to R) defined by (varphi: p(x) mapsto p(0)) is a surjective homomorphism with kerned ((x)). By the first isomorphism theorem, we have (R[x]/(x) cong R). Furthermore, ((x)) is a maximal ideal, is a prime ideal, and because (R[x]) is a principal ideal domain, ((x)) is maximal. Therefore (R[x]/(x)) is a field, so (R) is a field as well.



end{document}

You could start by experimenting with tcolorbox: find its documentation with texdoc tcolorbox at the terminal or on CTAN.