9. (a) Given that

$$\frac { x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x - 9 } { x ^ { 2 } - x - 12 } \equiv x ^ { 2 } + P + \frac { Q } { x - 4 } \quad x > - 3$$

find the value of the constant $P$ and show that $Q = 5$

The curve $C$ has equation $y = \mathrm { g } ( x )$, where

$$g ( x ) = \frac { x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x - 9 } { x ^ { 2 } - x - 12 } \quad - 3 < x < 3.5 \quad x \in \mathbb { R }$$

(b) Find the equation of the tangent to $C$ at the point where $x = 2$

Give your answer in the form $y = m x + c$, where $m$ and $c$ are constants to be found.

\begin{figure}[h]
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  \includegraphics[alt={},max width=\textwidth]{96948fd3-5438-4e95-b41b-2f649ca8dfac-28_876_961_1055_495}
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\caption{Figure 4}
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Figure 4 shows a sketch of the curve $C$.\\
The region $R$, shown shaded in Figure 4, is bounded by $C$, the $y$-axis, the $x$-axis and the line with equation $x = 2$\\
(c) Find the exact area of $R$, writing your answer in the form $a + b \ln 2$, where $a$ and $b$ are constants to be found.

\includegraphics[max width=\textwidth, alt={}, center]{96948fd3-5438-4e95-b41b-2f649ca8dfac-31_2255_50_314_34}\\

\begin{center}
\begin{tabular}{|l|l|l|}
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VIHV SIHII NI I IIIM I ON OC & VIAV SIHI NI JYHAM ION OO & VI4V SIHI NI JLIYM ION OO \\
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\end{center}

\includegraphics[max width=\textwidth, alt={}, center]{96948fd3-5438-4e95-b41b-2f649ca8dfac-32_106_113_2524_1832}

\hfill \mbox{\textit{Edexcel P3 2020 Q9 [14]}}