I would like to display:
I. Factor completely.
1. some polynomial
2. some other polynomial
II. Reduce each expression.
3. some rational expression
4. some other rational expression
But I would like to keep the numbering running throughout each section, so if I add another question to a section I don't have to re-number everything. I know if I use \begin{questions} \end{questions} that I can do this, but then I can't insert the section number and the instructions. Or at least, I don't know how to.

enumitempackage, tonight! ;-) I think it’s better to define aseries, here, just in case some other, unrelatedenumerateenvironment occurs in between. – GuM Jun 08 '17 at 20:08