| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Type | Partial Fraction Form via Division |
| Difficulty | Moderate -0.3 This is a straightforward polynomial long division question requiring systematic algebraic manipulation to find constants. While it involves a quartic divided by a quadratic (requiring two division steps), it's a standard C4 technique with no conceptual difficulty—just careful arithmetic. The method is routine and well-practiced, making it slightly easier than average. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division |
\begin{enumerate}
\item $\mathrm { f } ( x ) = \frac { x ^ { 4 } + x ^ { 3 } - 13 x ^ { 2 } + 26 x - 17 } { x ^ { 2 } - 3 x + 3 }$.
\end{enumerate}
Find the values of the constants $A , B , C$ and $D$ such that
$$f ( x ) = x ^ { 2 } + A x + B + \frac { C x + D } { x ^ { 2 } - 3 x + 3 }$$
\hfill \mbox{\textit{OCR C4 Q1 [4]}}