9.
$$g ( x ) = 4 x ^ { 3 } - 12 x ^ { 2 } - 15 x + 50$$
- Use the factor theorem to show that \(( x + 2 )\) is a factor of \(\mathrm { g } ( x )\).
- Hence show that \(\mathrm { g } ( x )\) can be written in the form \(\mathrm { g } ( x ) = ( x + 2 ) ( a x + b ) ^ { 2 }\), where \(a\) and \(b\) are integers to be found.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f7935caa-6626-4ba8-87ef-e9bb59e1ac3e-22_517_807_607_621}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation \(y = \mathrm { g } ( x )\) - Use your answer to part (b), and the sketch, to deduce the values of \(x\) for which
- \(\mathrm { g } ( x ) \leqslant 0\)
- \(\mathrm { g } ( 2 x ) = 0\)