Align-like environment in a column of array

Question

I have an array in which one of the columns is a polynomial, and I would like to align the terms of the polynomial for each row of the array. My hack is to use \phantoms all over the place, but is there a way to do this automatically? For instance, if I could make this part of the array act like some sort of align environment?

Here is a MWE:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

What I have:
\[ \begin{array}{|r|c|}
\hline
S & P(x) \\ 
\hline
9 & x + x^2 + x^3 \\
10 & 3x + x^2 + x^3 \\
11 & x + 10x^3\\
\hline
\end{array} \]

What I want:
\[ \begin{array}{|r|c|}
\hline
S & P(x) \\ 
\hline
9 & \phantom{3}x + x^2 + \phantom{10}x^3 \\
10 & 3x + x^2 + \phantom{10}x^3 \\
11 & \phantom{3}x \phantom{{} + x^2 } + 10x^3\\
\hline
\end{array} \]

\end{document}

Answer 1

You can use more columns like

\[ \begin{array}{|r|r@{{}+{}}c@{{}+{}}r|}
\hline
S & \multicolumn{3}{|c|}{P(x)} \\
\hline
9  & x                      & x^2   &x^3 \\
10 & 3x                     & x^2   & x^3 \\
11 &  \mc{x} &       & 10x^3\\
\hline
\end{array} \]

where \mc is defined to take care of alignment without the succeding + sign.

Code:

\documentclass{article}
\usepackage{amsmath}
\newlength{\mylen}
\settowidth{\mylen}{${}+{}$}
\newcommand{\mc}[1]{\multicolumn{1}{r@{\hspace{\mylen}}}{#1}}
\begin{document}

What I have:
\[ \begin{array}{|r|c|}
\hline
S & P(x) \\
\hline
9 & x + x^2 + x^3 \\
10 & 3x + x^2 + x^3 \\
11 & x + 10x^3\\
\hline
\end{array} \]

What I want:
\[ \begin{array}{|r|r@{{}+{}}c@{{}+{}}r|}
\hline
S & \multicolumn{3}{|c|}{P(x)} \\
\hline
9  & x                      & x^2   &x^3 \\
10 & 3x                     & x^2   & x^3 \\
11 &  \mc{x} &       & 10x^3\\
\hline
\end{array} \]

\end{document}