| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| 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 standard C2 polynomial question testing factor theorem and remainder theorem. Part (i) requires setting up two simultaneous equations from given conditions (routine application of theorems), and part (ii) involves verification and factorisation using the found root. The algebraic manipulation is straightforward with no conceptual challenges beyond direct application of learned techniques. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
The cubic polynomial $f(x)$ is given by
$$f(x) = x^3 + ax + b,$$
where $a$ and $b$ are constants. It is given that $(x + 1)$ is a factor of $f(x)$ and that the remainder when $f(x)$ is divided by $(x - 3)$ is 16.
\begin{enumerate}[label=(\roman*)]
\item Find the values of $a$ and $b$. [5]
\item Hence verify that $f(2) = 0$, and factorise $f(x)$ completely. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q5 [8]}}