| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | Factor & Remainder Theorem |
| Type | Verify factor then simplify rational expression |
| Difficulty | Standard +0.3 This is a straightforward two-part question requiring routine application of the factor theorem (substituting x = -1/2) followed by polynomial division and standard partial fractions decomposition. While it involves multiple steps, each technique is standard A-level fare with no novel insight required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02y Partial fractions: decompose rational functions |
\begin{enumerate}
\item In this question you must show all stages of your working.
\end{enumerate}
Solutions based entirely on calculator technology are not acceptable.
$$f ( x ) = 4 x ^ { 3 } - 4 x ^ { 2 } - 7 x - 2$$
a) Use the factor theorem to show that ( $2 x + 1$ ) is a factor of $f ( x )$.\\
b) Write $\frac { 3 x + 4 } { f ( x ) }$ in partial fraction form.\\
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q4 [6]}}