LaTeX 中的表格类型

Question

我正在尝试重现该表但遇到了困难。

我尝试过

\documentclass[a4paper,12pt,openany]{book}
\usepackage[table]{xcolor}
\setlength{\arrayrulewidth}{1mm}
\setlength{\tabcolsep}{18pt}
\renewcommand{\arraystretch}{2.5}
\newcolumntype{s}{>{\columncolor[HTML]{AAACED}} p{3cm}}
\arrayrulecolor[HTML]{DB5800}


\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{latexsym}
\usepackage{mathrsfs}

\usepackage{color}

\begin{document}
\begin{tabular}{ |p{10.5cm}|s| }
    \hline
    L'ensemble des polynômes de degré inférieur ou égal à $n$ & Notation : $\mathscr{P}_n$ ou $\mathbb{R}_n[X]$ \\
    \hline
    \rowcolor{lightgray} \multicolumn{2}{|c|}{$P \in \mathscr{P}_n$ signifie que $P$ est un polynôme de degré inférieur ou égal à $n$} \\
    $(\forall (P, Q) \in \mathscr{P}_n^2) \quad (\forall x \in \mathbb{R}) \quad \begin{cases}
            (P + Q)(x) = P(x) + Q(x) \\
            (P \times Q)(x) = P(x) \times Q(x)
        \end{cases}$ \\
    \hline
\end{tabular}
\end{document}

我得到了什么

Answer 1

像这样吗？

\documentclass[a4paper,12pt,openany]{book}
\usepackage[table,svgnames]{xcolor}
\usepackage{amsmath,amssymb,mathrsfs,calc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}

\setlength{\arrayrulewidth}{0.5mm} % '1mm' seems to be too much
\renewcommand{\arraystretch}{1.75} % '2.5' seems to be too much
\arrayrulecolor[HTML]{DB5800}

\begin{document}

\noindent
\begin{tabular}{%
   >{\raggedright\arraybackslash}p{0.62\textwidth-2\tabcolsep-\arrayrulewidth} |
   >{\raggedright\arraybackslash}p{0.38\textwidth-2\tabcolsep} }
\hline
L'ensemble des polynômes de degré inférieur ou égal à $n$ & 
Notation: $\mathscr{P}_n$ ou $\mathbb{R}_n[X]$ \\
\hline
\rowcolor{Gainsboro} % a bit lighter than "lightgray" 
\multicolumn{2}{p{\textwidth-2\tabcolsep}}{%
$P\in\mathscr{P}_n$ signifie que $P$ est un polynôme de degré inférieur ou égal à $n$ 

\[
  \forall (P, Q) \in \mathscr{P}_n^2) \quad 
      (\forall x \in \mathbb{R}) \quad 
      \left\{ \begin{aligned}
                &(P + Q)(x) = P(x) + Q(x) \\
                &(P \times Q)(x) = P(x) \times Q(x)
      \end{aligned} \right.
\] } \\
\hline
\end{tabular}

\end{document}