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I know there exists a standard code for a Horner scheme. But I would like to get the following tabular.

enter image description here

I've got the next code but I can't find how I get that little vertical line at the right bottom.

\begin{tabular}{c|cccc}  
        & 3 & 2 & -5 & -10 \\   
    &   &   &    &     \\ \hline  
        &   &   &    &    
\end{tabular}  

I've got another question about this. The number 11 is now shifted to the left, but I want that it's under 16.

\begin{tabular}{c|cccc}  
  & 3 & 2 & -5 & -10 \\   
  2 & $\downarrow$  & 6  & 16    & 22   \\ \hline  
  & 3  & 8  &  11   \multicolumn{1}{c|}{}  & 12   
\end{tabular}
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You should use \[ \begin{array}{c|rrrr} & 3 & 2 & -5 & -10 \\ 2 & \downarrow & 6 & 16 & 22 \\ \hline & 3 & 8 & \multicolumn{1}{c|}{11} & 12 \end{array} \] otherwise, minus signs will be considered as mere hyphens and the results won't be good. – Gonzalo Medina Mar 14 '14 at 18:11
    
Thank you! It works! – Silke Mar 15 '14 at 10:40
up vote 12 down vote accepted
\documentclass{article}
\begin{document}
  $\begin{array}{c|cccc}
        & 3 & 2 & -5 & -10 \\
    &   &   &    &     \\ \hline
        &   &   & \multicolumn{1}{c|}{}   &
\end{array}$
\end{document}

enter image description here

If you want it to be thick,

\documentclass{article}
\usepackage{array}
\begin{document}
  $\begin{array}{c|cccc}
        & 3 & 2 & -5 & -10 \\
    &   &   &    &     \\ \hline
        &   &   &    & \multicolumn{1}{!{\vrule width 1.5pt}c}{}
\end{array}$
\end{document}

enter image description here

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1  
You should use array or math mode for the entries anyway. – egreg Mar 14 '14 at 16:32
1  
The negative sign looks bad in text mode. :-) – kiss my armpit Mar 14 '14 at 17:41

Just for fun, a macro that also computes the coefficients (only integers allowed).

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\horner}{smm}
 {
  \IfBooleanTF{#1}
   { \bool_set_false:N \l_silke_show_bool }
   { \bool_set_true:N \l_silke_show_bool }
  \silke_horner:nn { #2 } { #3 }
 }

\bool_new:N \l_silke_show_bool
\seq_new:N \l_silke_top_seq
\seq_new:N \l_silke_middle_seq
\seq_new:N \l_silke_bottom_seq
\seq_new:N \l_silke_temp_seq
\int_new:N \l_silke_degree_int
\tl_new:N \l_silke_remainder_tl

\cs_new_protected:Npn \silke_horner:nn #1 #2
 {
  \seq_set_split:Nnn \l_silke_top_seq { , } { #1 }
  \int_set:Nn \l_silke_degree_int { \seq_count:N \l_silke_top_seq }
  \seq_clear:N \l_silke_middle_seq
  \seq_clear:N \l_silke_bottom_seq
  \seq_put_right:Nn \l_silke_middle_seq { \downarrow }
  \seq_put_right:Nx \l_silke_bottom_seq
   {
    \int_to_arabic:n { \seq_item:Nn \l_silke_top_seq { 1 } }
   }
  \int_step_inline:nnnn { 2 } { 1 } { \l_silke_degree_int }
   {
    \seq_put_right:Nx \l_silke_middle_seq
     {
      \int_to_arabic:n { \seq_item:Nn \l_silke_bottom_seq { ##1 - 1 } * #2 }
     }
    \seq_put_right:Nx \l_silke_bottom_seq
     {
      \int_to_arabic:n
       {
        \seq_item:Nn \l_silke_top_seq { ##1 }
        +
        \seq_item:Nn \l_silke_middle_seq { ##1 }
       }
     }
   }
  \silke_print_scheme:n { #2 }
 }

\cs_new_protected:Npn \silke_print_scheme:n #1
 {
  \bool_if:NF \l_silke_show_bool
   {
    \silke_phantom:N \l_silke_middle_seq
    \silke_phantom:N \l_silke_bottom_seq
   }
  \seq_pop_right:NN \l_silke_bottom_seq \l_silke_remainder_tl
  \begin{array}{r | *{\l_silke_degree_int}{r} }
     & \seq_use:Nn \l_silke_top_seq { & } \\
  #1 & \seq_use:Nn \l_silke_middle_seq { & } \\
  \hline
     & \seq_use:Nn \l_silke_bottom_seq { & } & 
       \multicolumn{1}{@{\vline width 1pt}r}{\l_silke_remainder_tl}
  \end{array}
 }

\cs_new_protected:Npn \silke_phantom:N #1
 {
  \seq_clear:N \silke_temp_seq
  \seq_map_inline:Nn #1 { \seq_put_right:Nn \silke_temp_seq { \phantom{##1} } }
  \seq_set_eq:NN #1 \silke_temp_seq
 }

\ExplSyntaxOff

\begin{document}

$\horner{3,2,-5,-10}{2}$

$\horner*{3,2,-5,-10}{2}$

$\horner{1,5,10,10,5,1}{-1}$

\end{document}

The *-variant just reserves the space, but doesn't print the numbers in the middle and bottom rows.

enter image description here

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