| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Type | Sketching Polynomial Curves |
| Difficulty | Moderate -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. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
Given that $f(x) = (x^2 - 6x)(x - 2) + 3x$,
\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]}}