Word-wrapping page-long polynomials in latex

Displayed math can't be broken automatically, but in-line math can. So you can try something like

\newenvironment{polynomial}
  {\par\vspace{\abovedisplayskip}%
   \setlength{\leftskip}{\parindent}%
   \setlength{\rightskip}{\leftskip}%
   \medmuskip=4mu plus 2mu minus 2mu
   \binoppenalty=0
   \noindent$\displaystyle}
  {$\par\vspace{\belowdisplayskip}}

and put your long polynomial in the newly defined environment.

if you're using amsmath, there's a command \allowdisplaybreaks that would work in an align environment (though not in the aligned sub-environment). it's documented in the amsmath user's guide on pp.8-9. the recommendation is to put

\allowdisplaybreaks[1]

in your preamble if you want it to work throughout the document.