| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single polynomial, two remainder/factor conditions |
| Difficulty | Standard +0.3 This is a standard C2 polynomial question using the factor theorem and remainder theorem. Part (a) requires setting up two simultaneous equations by substituting x=1/2 and x=1, which is routine. Part (b) involves polynomial division and factorising a quadratic, all standard techniques. While it has multiple steps (9 marks total), each step follows directly from applying well-practiced methods with no novel insight required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$f(x) = 6x^3 + px^2 + qx + 8$, where $p$ and $q$ are constants.
Given that $f(x)$ is exactly divisible by $(2x - 1)$, and also that when $f(x)$ is divided by $(x - 1)$ the remainder is $-7$,
\begin{enumerate}[label=(\alph*)]
\item find the value of $p$ and the value of $q$. [6]
\item Hence factorise $f(x)$ completely. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [9]}}