| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Find constant then solve inequality or further work |
| Difficulty | Moderate -0.8 This is a straightforward application of the Factor Theorem requiring simple substitution (f(1)=0 to find p) followed by routine use of the Remainder Theorem (evaluate f(-1/2)). Both parts are direct recall of standard techniques with minimal algebraic manipulation, making it easier than the average A-level question which typically requires more problem-solving or multi-step reasoning. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 1 | 2 |
Question 1:
1 | 1 | 2 | 2 | 4$f(x) = 2x^3 - x^2 + px + 6$,
where $p$ is a constant.
Given that $(x - 1)$ is a factor of $f(x)$, find
\begin{enumerate}[label=(\alph*)]
\item the value of $p$, [2]
\item the remainder when $f(x)$ is divided by $(2x + 1)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q1 [4]}}