| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single polynomial, two remainder/factor conditions |
| Difficulty | Moderate -0.3 This is a straightforward application of the Remainder Theorem and Factor Theorem from C2. Part (a) requires substituting x=1 and setting equal to 9 (standard recall), while part (b) involves substituting x=-2 and setting equal to 0, then solving simultaneous equations. The algebraic manipulation is routine with no conceptual challenges, making it slightly easier than average but not trivial since it requires multiple steps and careful arithmetic. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$f(x) = ax^3 + bx^2 - 7x + 14$, where $a$ and $b$ are constants.
Given that when $f(x)$ is divided by $(x - 1)$ the remainder is 9,
\begin{enumerate}[label=(\alph*)]
\item write down an equation connecting $a$ and $b$. [2]
\end{enumerate}
Given also that $(x + 2)$ is a factor of $f(x)$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the values of $a$ and $b$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q2 [6]}}