| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Trigonometric substitution equations |
| Difficulty | Standard +0.3 This is a straightforward multi-part question combining routine factor theorem application, polynomial factorization by division, and a simple trigonometric substitution. Part (a) is pure verification, part (b) is standard algebraic division followed by factoring a quadratic, and part (c) only requires substituting tan θ = x, solving for x values, then applying arctan in the specified range. No novel insight required, just methodical application of standard techniques. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.05o Trigonometric equations: solve in given intervals |
3.
$$f ( x ) = 6 x ^ { 3 } + 17 x ^ { 2 } + 4 x - 12$$
\begin{enumerate}[label=(\alph*)]
\item Use the factor theorem to show that ( $2 x + 3$ ) is a factor of $\mathrm { f } ( x )$.
\item Hence, using algebra, write $\mathrm { f } ( x )$ as a product of three linear factors.
\item Solve, for $\frac { \pi } { 2 } < \theta < \pi$, the equation
$$6 \tan ^ { 3 } \theta + 17 \tan ^ { 2 } \theta + 4 \tan \theta - 12 = 0$$
giving your answers to 3 significant figures.
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P2 2020 Q3 [8]}}