Edexcel C1 — Question 9 8 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks8
PaperDownload PDF ↗
TopicPolynomial Division & Manipulation
TypeSketching Polynomial Curves
DifficultyModerate -0.8 This is a straightforward C1 algebraic manipulation question requiring expansion, factorisation, and sketching. All steps are routine: expand brackets, collect terms, factor out common term, find roots, and plot. No problem-solving insight needed, just careful execution of standard techniques.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials

Given that \(f(x) = (x^2 - 6x)(x - 2) + 3x\),
  1. express \(f(x)\) in the form \(a(x^2 + bx + c)\), where \(a\), \(b\) and \(c\) are constants. [3]
  2. Hence factorise \(f(x)\) completely. [2]
  3. Sketch the graph of \(y = f(x)\), showing the coordinates of each point at which the graph meets the axes. [3]

Given that $f(x) = (x^2 - 6x)(x - 2) + 3x$,

\begin{enumerate}[label=(\alph*)]
\item express $f(x)$ in the form $a(x^2 + bx + c)$, where $a$, $b$ and $c$ are constants. [3]
\item Hence factorise $f(x)$ completely. [2]
\item Sketch the graph of $y = f(x)$, showing the coordinates of each point at which the graph meets the axes. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C1  Q9 [8]}}