| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | October |
| Marks | 7 |
| Topic | Factor & Remainder Theorem |
| Type | Single polynomial, two remainder/factor conditions |
| Difficulty | Moderate -0.3 This is a straightforward application of the factor theorem and simultaneous equations. Part (a) requires substituting x=2 and x=-3 to form two linear equations in b and c, then solving them. Part (b) simply requires factoring out (x-2) from the result. The algebra is routine with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$f(x) = x^4 + bx + c$
$(x-2)$ is a factor of $f(x)$.
$f(-3) = 35$.
\begin{enumerate}[label=(\alph*)]
\item Find $b$ and $c$. [4]
\item Hence express $f(x)$ as the product of linear and cubic factors. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q10 [7]}}