10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb21001f-fe68-4776-992d-ede1aae233d7-26_902_896_248_587}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of part of the curve \(C\) with equation \(y = \mathrm { f } ( x )\), where
$$f ( x ) = ( 3 x + 20 ) ( x + 6 ) ( 2 x - 3 )$$
- Use the given information to state the values of \(x\) for which
$$f ( x ) > 0$$
- Expand \(( 3 x + 20 ) ( x + 6 ) ( 2 x - 3 )\), writing your answer as a polynomial in simplest form.
The straight line \(l\) is the tangent to \(C\) at the point where \(C\) cuts the \(y\)-axis.
Given that \(l\) cuts \(C\) at the point \(P\), as shown in Figure 4, - find, using algebra, the \(x\) coordinate of \(P\)
(Solutions based on calculator technology are not acceptable.)