1

I've tried to create a polynomial long division using several approaches such as the ones outlined in:

How to draw polynom division?

Polynomial Long Division Using Polynom

Better way to display long division?

With limited success. So I tried the naive approach which looks quite good as can be seen in the diagram, however, the vertical bar \big| is spaced too far down. If possible I'd like it to move up and ideally touch the horizontal long division bar.

How can I accomplish this?

\documentclass[12pt,a4paper]{article}

\usepackage[fleqn]{amsmath}
\usepackage[normalem]{ulem}

\begin{document}
\begin{equation*}
\begin{split}
&\uline{x^4  + \theta x^3 + \theta^2x^2 + \theta^3x + \theta^4}\\
x - \theta \ \big| & x^5 -2\\
& \uline{x^5 - \theta x^4} \\
& \theta x^4 - 2\\
& \uline{\theta x^4 - \theta^2x^3}\\
& \theta^2x^3 - 2\\
& \uline{\theta^2x^3 - \theta^3x^2}\\
& \theta^3x^2 - 2\\
&\uline{\theta^3x^2 - \theta^4x}\\
& \theta^4x - 2\\
& \uline{\theta^4x - \theta^5}\\
& \theta^5 - 2  \ \ \ \ \ \ \ \ \ =  \ \ \ 0
\end{split}
\end{equation*}

\end{document}

Which produces:

polynomial division

3

I propose one of these layouts, based on array, alignedat and booktabs:

\documentclass[12pt,a4paper]{article}
\usepackage{array}
\usepackage[fleqn]{amsmath}
\usepackage{booktabs}

\begin{document}

\begin{equation*}\setlength\extrarowheight{3pt}
  \begin{array}{rl}
    & x⁴ + θx³ + \theta²x² + \theta³x + \theta⁴ \\
    \cmidrule(r{4em}){2-2}\addlinespace[-\dimexpr\belowrulesep + \cmidrulewidth]
    \multicolumn{1}{r!{\rule[-2ex]{0.4pt}{5ex}}}{x - θ} & \begin{alignedat}[t]{8}
      & \phantom{-}x⁵ & & & & & & & & & {} - {} & 2 \\%[1ex]
    &{-} x⁵ + {}& & θx⁴ \\
    \cmidrule(r{3.5em}){1-12}
      & & & θx⁴ & & & & & & & {}-{} & 2 \\
    & &- & θx⁴ & {} + {}&\theta²x³\\
    \cmidrule(r{3.5em}){3-12}
      & & & & & \theta²x³ & & & & & {}-{} & 2 \\
    & & & &- & \theta²x³ & {} + {} & \theta³x²\\
    \cmidrule(l{0.5em}r{3.5em}){5-12}
      & & & & & & & \theta³x² & & & {}-{} & 2 \\
    & & & & & & -&\theta³x² & {} + {} & \theta⁴x\\
    \cmidrule(l{0.5em}r{3.5em}){7-12}
      & & & & & & & & & \theta⁴x & {}-{} & 2 \\
      & & & & & & & & & \theta⁴x & {}-{} & \theta⁵ \\
    \cmidrule(l{1em}r{3.5em}){9-12}
      & & & & & & & & & & & \theta⁵ - 2 = 0
    \end{alignedat}
  \end{array}
\end{equation*}

\begin{equation*}\setlength\extrarowheight{3pt}
  \begin{array}{rl}
    & x⁴ + θx³ + \theta²x² + \theta³x + \theta⁴ \\
    \cmidrule(r{7.5em}){2-2}\addlinespace[-\dimexpr\belowrulesep + \cmidrulewidth]
    \multicolumn{1}{r|}{x - θ} &
    \phantom{-}x⁵ - 2\\[1ex]
    & \begin{alignedat}[t]{8}
    -&x⁵ &{}+{} & θx⁴ \\
    \cmidrule(r{1em}){1-6}
    & & & θx⁴ & {}-{} & 2\\
    & & -& θx⁴ & {} + {}&\theta²x³\\
    \cmidrule(lr{1em}){3-8}
    & & & & & \theta²x³ & {}-{} & 2\\
    & & & &- & \theta²x³ & {} + {} & \theta³x²\\
    \cmidrule(lr{0.5em}){5-10}
    & & & & & & & \theta³x² & {} - {} & 2\\
    & & & & & & - &\theta³x² & {} + {} & \theta⁴x\\
    \cmidrule(lr{3.5em}){7-12}
      & & & & & & & & & \theta⁴x & {}-{} & 2 \\
      & & & & & & & & - & \theta⁴x & {} + {} & \theta⁵ \\
    \cmidrule(l{-0.5em}r{1.5em}){12-12}
      & & & & & & & & & & & \theta⁵ - 2 = 0
    \end{alignedat}
  \end{array}
\end{equation*}

\end{document} 

enter image description here

1

Polynomial devision is (sometimes at least) clearer if you align the monomial terms, so here I take three cells per monomial r for the coefficient, l for the power of x and c for the binary operator.

Touching the line is achieved with \vline which is the segment latex usually uses for vertical rules in tables as specified by a | in the array or tabular preamble.

enter image description here

\documentclass[12pt,a4paper]{article}
\usepackage{array}
\usepackage[fleqn]{amsmath}


\begin{document}

\begin{equation*}
\setlength\arraycolsep{0pt}
\setlength\extrarowheight{2pt}
\begin{array}{r@{\;}c@{\;}*{10}{rl>{{}}c<{{}}}}
&&&&&&x^4&  +& \theta&x^3& +& \theta^2&x^2& +& \theta^3&x& +& \theta^4\\
\cline{2-18}
x - \theta &\vline& &x^5 &-&&&&&&&&&&&&&2\\
&& &x^5 &-& \theta &x^4 \\
\cline{3-18}
&&&&& \theta &x^4 &-&&&&&&&&&& 2\\
&&&&& \theta &x^4 &-& \theta^2&x^3\\
\cline{6-18}
&&&&&&&& \theta^2&x^3 &-& &&&&&&2\\
&&&&&&&& \theta^2&x^3 &-& \theta^3&x^2\\
\cline{9-18}
&&&&&&&&&&& \theta^3&x^2 &-&&&& 2\\
&&&&&&&&&&&\theta^3&x^2 &-& \theta^4&x\\
\cline{12-18}
&&&&&&&&&&&&&& \theta^4&x &-& 2\\
&&&&&&&&&&&&&& \theta^4&x &-& \theta^5\\
\cline{15-18}
&&&&&&&&&&&&&&&&& \theta^5 -2  &=  0
\end{array}
\end{equation*}

\end{document}

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.