| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Find remainder(s) then factorise |
| Difficulty | Moderate -0.8 This is a straightforward application of the remainder theorem (substitute x=2) followed by routine factorization using a given factor. Part (a) requires simple substitution, and part (b) involves polynomial division and factoring a quadratic—all standard C2 techniques with no problem-solving insight required. The 6 total marks reflect mechanical steps rather than conceptual difficulty. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$f(x) = 3x^3 - 5x^2 - 16x + 12$.
\begin{enumerate}[label=(\alph*)]
\item Find the remainder when $f(x)$ is divided by $(x - 2)$.
[2]
\end{enumerate}
Given that $(x + 2)$ is a factor of $f(x)$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item factorise $f(x)$ completely.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q2 [6]}}