| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single unknown from factor condition |
| Difficulty | Moderate -0.8 This is a straightforward application of the Factor Theorem requiring routine substitution to find c, polynomial division to factorize, and checking the discriminant of a quadratic. All steps are standard C2 techniques with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$$f(x) = x^3 - x^2 - 7x + c, \text{ where } c \text{ is a constant.}$$
Given that $f(4) = 0$,
\begin{enumerate}[label=(\alph*)]
\item Find the value of $c$, [2]
\item factorise $f(x)$ as the product of a linear factor and a quadratic factor. [3]
\item Hence show that, apart from $x = 4$, there are no real values of $x$ for which $f(x) = 0$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q13 [7]}}