| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | 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 and Factor Theorems requiring students to substitute x=1 and x=-2 into f(x), then solve two simultaneous linear equations in a and b. While it involves multiple steps (6 marks total), the techniques are standard C2 content 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 |
$$f(x) = ax^3 + bx^2 - 7x + 14, \text{ where } a \text{ and } b \text{ are constants.}$$
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 Q12 [6]}}