[Tex/LaTex] align long equation

align

I know this type of questions have been asked previously but I haven't found something to solve this problem. I have the following long code :

\documentclass[12pt,a4paper,twoside]{report}
\usepackage{amsmath,amsthm,mathtools}
\begin{document}
\begin{align*}
f_{32}=&x^{32} +12198x^{31} +2314465x^{30} -12105775188x^{29} +5363823023298x^{28} +112255815323746\\
&8x^{27} -1190957568896565522x^{26} +209082600175304589984x^{25} +22989403151925296937\\
&003x^{24} -4914900851027091491992374x^{23} +187314971305181007593402091x^{22} +185143\\
&5573081259757991725916x^{21} -177112654221172660874138268072x^{20} +43926953348772\\
&854958076288336008x^{19} -8069925182155695353376402378426972x^{18} +68958542881736\\
&5840411341429649636128x^{17} -23740614034450231197314286171021009177x^{16} -155324\\
&9919261394918300632995703368436966x^{15} +25870940606770260632602122011252618896\\
&6887x^{14} -14511399786110161424357109505278330297341724x^{13} +1463537885226408987\\
&41319428949250465719024858x^{12} +32750278659384832647975670671061051222933180188\\
&x^{11} -2286974864798158343157856729712480557839267556386x^{10} +5932631975811948614\\
&5828221766889960355126201846912x^9 +6575146802218754701624346687966744930450753\\
&36579853x^8 -105521419234945522100651241454885243895292286754573898x^7 +40112381\\
&65200337244745440754326620606602486694989793197x^6 -886067081083651605769689130\\
&22740501751611649852083140204x^5 +127506445946767356976971370547537041919975453\\
&7492781650348x^4 -12161035278122430054818848726808537446643676687311798879424x^3\\
 &+74518442436178190616718411536731834197503633925706662198320x^2 -2668848018838\\
&36189911937468492568061745225307284731520442304x +4266570219847726085064384156\\
&02232517825896105800369395838016
\end{align*}
\end{document}

The problem here is that I try to adjust the end of the equation by inserting \\ and & wherever it is appropriate to split the equations into multiple lines, unfortunately it looks messy and not aligned at all. I have insert an image with red circle identifying my problem.
enter image description here

Best Answer

In my opinion, in order to preserve some semblance of readability of this polynomial expression, you should have only one term per line for virtually all terms. For sure, don't introduce line breaks in the long integer terms.

enter image description here

\documentclass[12pt,a4paper,twoside]{report}
\usepackage{amsmath}
\allowdisplaybreaks % allow page breaks
\begin{document}
\begin{align*}
f_{32} &=x^{32} +12198x^{31} \\
&\quad+2314465x^{30} \\
&\quad-12105775188x^{29} \\
&\quad+5363823023298x^{28} \\
&\quad+1122558153237468x^{27} \\
&\quad -1190957568896565522x^{26} \\
&\quad+209082600175304589984x^{25}\\ 
&\quad+22989403151925296937003x^{24} \\
&\quad-4914900851027091491992374x^{23}\\ 
&\quad+187314971305181007593402091x^{22} \\
&\quad+1851435573081259757991725916x^{21}\\ 
&\quad-177112654221172660874138268072x^{20} \\
&\quad+43926953348772854958076288336008x^{19}\\ 
&\quad-8069925182155695353376402378426972x^{18} \\
&\quad+689585428817365840411341429649636128x^{17}\\ 
&\quad-23740614034450231197314286171021009177x^{16} \\
&\quad-1553249919261394918300632995703368436966x^{15}\\ 
&\quad+258709406067702606326021220112526188966887x^{14}\\ 
&\quad-14511399786110161424357109505278330297341724x^{13}\\ 
&\quad+146353788522640898741319428949250465719024858x^{12}\\ 
&\quad+32750278659384832647975670671061051222933180188x^{11}\\ 
&\quad-2286974864798158343157856729712480557839267556386x^{10}\\ 
&\quad+59326319758119486145828221766889960355126201846912x^9\\ 
&\quad+657514680221875470162434668796674493045075336579853x^8\\ 
&\quad-105521419234945522100651241454885243895292286754573898x^7\\ 
&\quad+4011238165200337244745440754326620606602486694989793197x^6\\ 
&\quad-88606708108365160576968913022740501751611649852083140204x^5 \\
&\quad+1275064459467673569769713705475370419199754537492781650348x^4 \\
&\quad-12161035278122430054818848726808537446643676687311798879424x^3\\
&\quad+74518442436178190616718411536731834197503633925706662198320x^2 \\
&\quad-266884801883836189911937468492568061745225307284731520442304x \\
&\quad+426657021984772608506438415602232517825896105800369395838016
\end{align*}
\end{document}

Addendum to address a comment left by the OP: If it's known that the equation has to (and will) fit on a single page, you may want to use an array environment instead of an align* environment. The former has an advantage in terms of more tighter line spacing, making it more likely that the full polynomial expression will indeed fit on a single page.

enter image description here

\documentclass[12pt,a4paper,twoside]{report}
\begin{document}
\appendix
\section*{Appendix: More information on \boldmath $ f_{32}$}

The function $f_{32}$ is given by the following 32nd-degree polynomial in $x$:
\[
\begin{array}{@{}r@{}l@{}}
f_{32} ={} &x^{32}\\
&{}+12198\,x^{31}\\
&{}+2314465\,x^{30}\\
&{}-12105775188\,x^{29}\\
&{}+5363823023298\,x^{28}\\
&{}+1122558153237468\,x^{27}\\
&{}-1190957568896565522\,x^{26}\\
&{}+209082600175304589984\,x^{25}\\ 
&{}+22989403151925296937003\,x^{24}\\
&{}-4914900851027091491992374\,x^{23}\\ 
&{}+187314971305181007593402091\,x^{22}\\
&{}+1851435573081259757991725916\,x^{21}\\ 
&{}-177112654221172660874138268072\,x^{20}\\
&{}+43926953348772854958076288336008\,x^{19}\\ 
&{}-8069925182155695353376402378426972\,x^{18}\\
&{}+689585428817365840411341429649636128\,x^{17}\\ 
&{}-23740614034450231197314286171021009177\,x^{16}\\
&{}-1553249919261394918300632995703368436966\,x^{15}\\ 
&{}+258709406067702606326021220112526188966887\,x^{14}\\ 
&{}-14511399786110161424357109505278330297341724\,x^{13}\\ 
&{}+146353788522640898741319428949250465719024858\,x^{12}\\ 
&{}+32750278659384832647975670671061051222933180188\,x^{11}\\ 
&{}-2286974864798158343157856729712480557839267556386\,x^{10}\\ 
&{}+59326319758119486145828221766889960355126201846912\,x^9\\ 
&{}+657514680221875470162434668796674493045075336579853\,x^8\\ 
&{}-105521419234945522100651241454885243895292286754573898\,x^7\\ 
&{}+4011238165200337244745440754326620606602486694989793197\,x^6\\ 
&{}-88606708108365160576968913022740501751611649852083140204\,x^5\\
&{}+1275064459467673569769713705475370419199754537492781650348\,x^4\\
&{}-12161035278122430054818848726808537446643676687311798879424\,x^3\\
&{}+74518442436178190616718411536731834197503633925706662198320\,x^2\\
&{}-266884801883836189911937468492568061745225307284731520442304\,x\\
&{}+426657021984772608506438415602232517825896105800369395838016
\end{array}
\]
\end{document}
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