MathWit entry/demo course - Math0

Here is the first example of long division. You can run it on the website (or a website you prefer): 

https://www.overleaf.com/ (now requires login)

https://latexbase.com (currently no login is needed)

If you have latex installed on your computer, that would be best since it can be faster and you will have more control. 

A code that barely works is here, if you are not patient enough, you can skip this and go all the way near the end:

$ \begin{array}{ccccccccccc} & & & & & x^4 & +x^3 & -x^2 &-x &\\ \cline{3-10} \multicolumn{2}{r}{x^3+x+1 \surd} & x^7 &+x^6 & &+x^4& &+x^2 &+x & +1& \\ & &x^7& &+x^5&+x^4& & & & \\ \cline{3-7} & & &x^6&-x^5 & & & & & \\ & & &x^6& &+x^4&+x^3& & & \\ \cline{4-8} & & & & -x^5&-x^4 &-x^3&+x^2& & \\ & & & &-x^5 & &-x^3&-x^2& & \\ \cline{5-9} & & & & &-x^4 & &+2x^2& +x& \\ & & & & &-x^4 & &-x^2& -x& \\ \cline{6-10} & & & & & & &3x^2& +2x&+1 \\ \end{array} $

The output should be looks like this, but with a gap to the right of the radical sign.

You may use arraystretch to adjust the space. The above picture shows the result of a stretch by a factor of1.1. 

\begingroup \renewcommand*{\arraystretch}{1.1} $\begin{array}{ccccccccccc} & & & & & x^4 & +x^3 & -x^2 &-x &\\ \cline{3-10} \multicolumn{2}{r}{x^3+x+1 \surd} & x^7 &+x^6 & &+x^4& &+x^2 &+x & +1& \\ & &x^7& &+x^5&+x^4& & & & \\ \cline{3-7} & & &x^6&-x^5 & & & & & \\ & & &x^6& &+x^4&+x^3& & & \\ \cline{4-8} & & & & -x^5&-x^4 &-x^3&+x^2& & \\ & & & &-x^5 & &-x^3&-x^2& & \\ \cline{5-9} & & & & &-x^4 & &+2x^2& +x& \\ & & & & &-x^4 & &-x^2& -x& \\ \cline{6-10} & & & & & & &3x^2& +2x&+1 \\ \end{array}$ \endgroup

A nice fix with the complete latex code, with comments(removed system genereated strings, so it can compile without errors now):

\documentclass{article} \usepackage{amsmath,amssymb,array} \title{Math - Long Division Latex code} \author{Mathwit.com} \date{June $9999$} % Reference https://tex.stackexchange.com/questions/123731/replicate-a-typesetting-of-polynomial-long-division \begin{document} \maketitle \begin{align*} \renewcommand\arraystretch{.75}\renewcommand\arraycolsep{3pt} \begin{array}{r@{\hskip\arraycolsep}c@{\hskip\arraycolsep}l*5r} % n=8=3+5 &&0.&6&6&6&6&\cdots\\ \cline{2-8} %n=8 3&\Bigg)&2.&0&0&0&0&\cdots \\ &&1.&8&&&& \\ \cline{3-8}\\ &&&2&0&&&\\ &&&1&8&&&\\ \cline{4-8}\\ &&&&2&0&&\\ &&&&1&8&&\\ \cline{5-8}\\ &&&&&2&0&\\ &&&&&1&8&\\ \cline{6-8}\\ &&&&&&2& \\ &&&&&&&\ddots \\ \end{array} \end{align*} \end{document}

It has 8 columns, n=8 (see the comments in the code and the reference link). The output should be looks like this:

As an exercise, modify the above code to get the output as in thhe following picture: