| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Given factor, find all roots |
| Difficulty | Moderate -0.8 This is a straightforward application of the remainder theorem (substitute x=2) followed by routine polynomial factorisation using a given factor. Both parts require only direct recall of standard techniques with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (a) \(f(2) = 24 - 20 - 32 + 12 = -16\) | M1 A1 | Attempt \(f(2)\) or \(f(-2)\); answer must appear in part (a) |
| (b) \((x+2)(3x^2 - 11x + 6)\) | M1 A1 | Division by \((x+2)\) to get quadratic with \(a\neq 0, b\neq 0\) |
| \((x+2)(3x-2)(x-3)\) | M1 A1 | Attempt to factorise quadratic; combining all 3 factors not required |
# Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| **(a)** $f(2) = 24 - 20 - 32 + 12 = -16$ | M1 A1 | Attempt $f(2)$ or $f(-2)$; answer must appear in part (a) |
| **(b)** $(x+2)(3x^2 - 11x + 6)$ | M1 A1 | Division by $(x+2)$ to get quadratic with $a\neq 0, b\neq 0$ |
| $(x+2)(3x-2)(x-3)$ | M1 A1 | Attempt to factorise quadratic; combining all 3 factors not required |
**Total: 6 marks**
---$$f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 16 x + 12$$
\begin{enumerate}[label=(\alph*)]
\item Find the remainder when $\mathrm { f } ( x )$ is divided by ( $x - 2$ ).
Given that $( x + 2 )$ is a factor of $\mathrm { f } ( x )$,
\item factorise $\mathrm { f } ( x )$ completely.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2007 Q2 [6]}}