5.
$$f ( x ) = - 4 x ^ { 3 } + 16 x ^ { 2 } - 13 x + 3$$
- Use the remainder theorem to find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 1\) ).
- Use the factor theorem to show that ( \(x - 3\) ) is a factor of \(\mathrm { f } ( x )\).
- Hence fully factorise \(\mathrm { f } ( x )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08b1be3e-2d9a-4832-b230-d5519540f494-12_581_636_731_657}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\). - Use your answer to part (c) and the sketch to deduce the set of values of \(x\) for which \(\mathrm { f } ( x ) \leqslant 0\)