| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Two unknowns, direct system |
| Difficulty | Moderate -0.3 This is a standard C2 Factor/Remainder Theorem question requiring straightforward application of f(3)=14 and f(-1)=-18 to form simultaneous equations, then solving for a and b. Part (b) is routine verification by substitution. While it involves multiple steps (7 marks total), the techniques are purely procedural with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$$f(x) = x^3 + ax^2 + bx - 10, \text{ where } a \text{ and } b \text{ are constants.}$$
When $f(x)$ is divided by $(x - 3)$, the remainder is 14.
When $f(x)$ is divided by $(x + 1)$, the remainder is $-18$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $a$ and the value of $b$. [5]
\item Show that $(x - 2)$ is a factor of $f(x)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q29 [7]}}