4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0b4165d-b8bb-419c-b75a-d6c0c2431510-08_687_775_248_646}
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\caption{Figure 1}
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Figure 1 shows a sketch of part of the curve \(C\) with equation \(y = \frac { 1 } { x + 2 }\)
- State the equation of the asymptote of \(C\) that is parallel to the \(y\)-axis.
- Factorise fully \(x ^ { 3 } + 4 x ^ { 2 } + 4 x\)
A copy of Figure 1, labelled Diagram 1, is shown on the next page.
- On Diagram 1, add a sketch of the curve with equation
$$y = x ^ { 3 } + 4 x ^ { 2 } + 4 x$$
On your sketch, state clearly the coordinates of each point where this curve cuts or meets the coordinate axes.
- Hence state the number of real solutions of the equation
$$( x + 2 ) \left( x ^ { 3 } + 4 x ^ { 2 } + 4 x \right) = 1$$
giving a reason for your answer.
\includegraphics[max width=\textwidth, alt={}]{c0b4165d-b8bb-419c-b75a-d6c0c2431510-09_800_1700_1053_185}
Only use the copy of Diagram 1 if you need to redraw your answer to part (c).