| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | One unknown constant: find it then solve |
| Difficulty | Moderate -0.3 This is a straightforward application of the factor theorem and polynomial division. Part (i) requires substituting x = -1 and solving for k (routine). Part (ii) involves factoring and solving a quadratic after division. Standard C2 content with clear method, slightly easier than average due to the given factor making it mechanical rather than requiring insight. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$$f(x) = x^3 + kx - 20.$$
Given that f(x) is exactly divisible by $(x + 1)$,
\begin{enumerate}[label=(\roman*)]
\item find the value of the constant $k$, [2]
\item solve the equation $f(x) = 0$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q2 [6]}}