Edexcel C2 — Question 2 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
TopicFactor & Remainder Theorem
TypeFind remainder(s) then factorise
DifficultyModerate -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.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

\(f(x) = 3x^3 - 5x^2 - 16x + 12\).
  1. Find the remainder when \(f(x)\) is divided by \((x - 2)\). [2]
Given that \((x + 2)\) is a factor of \(f(x)\),
  1. factorise \(f(x)\) completely. [4]

$f(x) = 3x^3 - 5x^2 - 16x + 12$.

\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]}}