How to typeset and annotate a polynomial long division

Question

I need to type a paper for a teacher, who hasn't seen the European division method, so that she could possibly use it in her curriculum.

I need something to look like this

x^2+4x+4       Box(x+2) 
-(x^2 + 2x)
----------------
2x+4 
-(2x + 4)
-----------------
0

Answer 1

Here is one way to do this:

Notes:

• The booktabs package was used to provide flexible horizontal rules.
• The \Ph macro uses \hphantom{)} to insert a horizontal space equivalent to the closing bracket to get things all aligned.

Code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{booktabs}
\usepackage{array}
\newcommand*{\Ph}{\hphantom{)}}%
\begin{document}
$\begin{array}{r@{} r@{} r r}
  x^2 &{}+4x\Ph&{}+4\Ph       &\fbox{$(x+2)$} \\
-(x^2 &{}+ 2x) &\\
\cmidrule{1-2}
      & 2x\Ph &{}+4\Ph\\
      &-(2x\Ph &{}+4) \\
\cmidrule{2-3}
      & &0\Ph
\end{array}$
\end{document}

Answer 2

Try looking at the package polynom.sty (CTAN, TeXdoc). It can even do the division for you.