[Tex/LaTex] How to format a long polynomial

Question

I have a long polynomial:

\documentclass{article}
%\usepackage{amsmath}% Loaded by mathtools
\usepackage{mathtools}
\begin{document}
$ f(z)=\frac{1}{382112640}(-306772802511648469920\eta^4z^4+762453974480763801600\eta^5z^4-1678626210368271790080\eta^5z^3-28510918043555533736160\eta^4z^3+11443138641451067779872\eta^3z^3-52164076923190540413504\eta^2z^2-78145258181161076156160\eta^5z^2-211306163712129371808450\eta^4z^2+228927087397104405937944\eta^3z^2+999881065017543109136462\eta^3z-317254092617698017425280\eta^5z-443761561344388063474665\eta^4z+82327155732241730770824\eta z-514623285385260545505123\eta^2z-1010535343560043404912120\eta^2-357788302700438191196160\eta^5-43808044579418934376632-214023244873618345872240\eta^4+11818373349781028\\
079\eta^3+347370177721463765064153\eta)/((417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001))$
\end{document}

How do I format such a long polynomial correctly?

Answer 1

I would use something like this

\documentclass{article}
%\usepackage{amsmath}% Loaded by mathtools
\usepackage{mathtools}
\begin{document}
Blah blah
\[f(z)=\frac{1}{382112640}\cdot\frac{A}{B}\]
where
\begin{align*}
    A=&\,-306772802511648469920\eta^4z^4+762453974480763801600\eta^5z^4\\
    &\,-1678626210368271790080\eta^5z^3-28510918043555533736160\eta^4z^3\\
    &\,+11443138641451067779872\eta^3z^3-52164076923190540413504\eta^2z^2\\
    &\,-78145258181161076156160\eta^5z^2-211306163712129371808450\eta^4z^2\\
    &\,+228927087397104405937944\eta^3z^2+999881065017543109136462\eta^3z\\
    &\,-317254092617698017425280\eta^5z-443761561344388063474665\eta^4z\\
    &\,+82327155732241730770824\eta z-514623285385260545505123\eta^2z\\
    &\,-1010535343560043404912120\eta^2-357788302700438191196160\eta^5\\
    &\,-43808044579418934376632-214023244873618345872240\eta^4\\
    &\,+11818373349781028079\eta^3+347370177721463765064153\eta
\end{align*}
and
\[B=(417420z^2-4169121z-15571312)(1546z+3537)(3092z+17001)\]
\end{document}