| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | November |
| Marks | 7 |
| Topic | Factor & Remainder Theorem |
| Type | Known polynomial, verify then factorise |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring routine algebraic manipulation: verify f(-2)=0, perform polynomial division to find the quadratic factor, then factorise and read off roots. All steps are standard textbook procedures with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
2.
$$\mathrm { f } ( x ) = x ^ { 3 } + 4 x ^ { 2 } + x - 6$$
\begin{enumerate}[label=(\alph*)]
\item Use the factor theorem to show that $( x + 2 )$ is a factor of $\mathrm { f } ( x )$.
\item Factorise f(x) completely.
\item Write down all the solutions to the equation
$$x ^ { 3 } + 4 x ^ { 2 } + x - 6 = 0$$
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q2 [7]}}