Figure + table wider than textwidth

Question

I have a figure and a table placed next to one another, but they are wider than the textwidth. Now I want to center them so they exceed the textwidth margins. Can this be done?

Edit: currently I have something like this, but I can't seem to get this wider than the textwidth.

\begin{figure}
\begin{floatrow}
\ffigbox{%
 \includegraphics[height=5cm]{figure}
}{%
  \caption{figure caption}%
  \label{figure}
}
\capbtabbox{%
\begin{tabular}{ |c|}
  HERE COMES THE TABLE
\end{tabular}
}{%
  \caption{table}%
}
\end{floatrow}
%\vspace{-1cm}
\end{figure}

Answer 1

Using \DeclareMarginSet, you can declare a margin set allowing you to hang the object on both margins (there are predefined settings hangleft, hangright for each margin individually, but not for both of them simultaneouly); then, you can invoke this margin set together with an appropriate value for floatwidth and rowfill=yes. Something along these lines:

\documentclass{article}
\usepackage{graphicx}
\usepackage{floatrow}
\usepackage{lipsum}% just to generate text for the example

\DeclareMarginSet{hangboth}{\setfloatmargins*{\hskip-4cm}{\hskip-4cm}}

\begin{document}

\thisfloatsetup{floatwidth=\paperwidth,rowfill=yes,margins=hangboth}
\lipsum[4]
\begin{figure}[!ht]\CenterFloatBoxes
\begin{floatrow}
\ffigbox[\FBwidth]
  {\includegraphics[width=10cm,height=4cm]{example-image-a}}
  {\caption{figure caption}\label{figure}}
\ttabbox[\FBwidth]
  {\begin{tabular}{lll}
  column1a & column2a & column3a \\
  column1b & column2b & column3b \\
  column1c & column2c  & column3c \\
  column1d & column2d & column3d
  \end{tabular}}
  {\caption{table}}
\end{floatrow}
\end{figure}
\lipsum[4]

\end{document}

The option [!ht] was only used for the example; I am bot recommending its use.

To have the caption for the table below it (although it's usual for table captions to appear above the table), you can use \floatbox instead of \ttabbox for the table and perhaps do some additional adjustment for the vertical alignment using heightadjust and valign:

\documentclass{article}
\usepackage{graphicx}
\usepackage[rawfloats]{floatrow}
\usepackage{lipsum}

\DeclareMarginSet{hangboth}{\setfloatmargins*{\hskip-4cm}{\hskip-4cm}}

\begin{document}

\thisfloatsetup{floatwidth=\paperwidth,rowfill=yes,margins=hangboth,heightadjust=all,valign=b}
\lipsum[4]
\begin{figure}[!ht]
\begin{floatrow}
\ffigbox[\FBwidth]
  {\includegraphics[width=10cm,height=4cm]{example-image-a}}
  {\caption{figure caption}\label{figure}}
\floatbox{table}[\FBwidth]
  {\caption{table}}
  {\begin{tabular}{lll}
  column1a & column2a & column3a \\
  column1b & column2b & column3b \\
  column1c & column2c & column3c \\
  column1d & column2d & column3d
  \end{tabular}}
\end{floatrow}
\end{figure}
\lipsum[4]

\end{document}