| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Known polynomial, verify then factorise |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring substitution of x=-4 to verify the factor, followed by polynomial division and factorising a quadratic. It's routine C2 material with clear steps and no problem-solving insight needed, making it easier than average but not trivial since it requires accurate algebraic manipulation across multiple steps. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Attempt to evaluate \(f(-4)\) or \(f(4)\) | M1 | |
| \(f(-4) = 2(-4)^3 + (-4)^2 - 25(-4) + 12 = (-128+16+100+12) = 0\), so \(\ldots\) is a factor | A1 | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((x+4)(2x^2 - 7x + 3)\) | M1 A1 | First M requires \((2x^2 + ax + b)\), \(a \neq 0\), \(b \neq 0\) |
| \((2x-1)(x-3)\) | M1 A1 | Second M for attempt to factorise the quadratic. Total: 4 |
## Question 3:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Attempt to evaluate $f(-4)$ or $f(4)$ | M1 | |
| $f(-4) = 2(-4)^3 + (-4)^2 - 25(-4) + 12 = (-128+16+100+12) = 0$, so $\ldots$ is a factor | A1 | **Total: 2** |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(x+4)(2x^2 - 7x + 3)$ | M1 A1 | First M requires $(2x^2 + ax + b)$, $a \neq 0$, $b \neq 0$ |
| $(2x-1)(x-3)$ | M1 A1 | Second M for attempt to factorise the quadratic. **Total: 4** |
---\begin{enumerate}[label=(\alph*)]
\item Use the factor theorem to show that $( x + 4 )$ is a factor of $2 x ^ { 3 } + x ^ { 2 } - 25 x + 12$.
\item Factorise $2 x ^ { 3 } + x ^ { 2 } - 25 x + 12$ completely.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2005 Q3 [6]}}