| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single unknown from factor condition |
| Difficulty | Moderate -0.3 Part (a) is straightforward application of the factor theorem (substitute x=3/2 and solve for a), requiring only basic algebra. Part (b) requires factorization and analyzing a quadratic discriminant, which is standard P2 content but involves multiple routine steps. Overall slightly easier than average due to being a textbook application with clear signposting. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
I'd be happy to help clean up mark scheme content, but the content you've provided appears to be a data table or stem-and-leaf plot rather than a mark scheme with marking annotations (M1, A1, B1, etc).
Could you please provide the actual mark scheme content that needs to be cleaned up? A mark scheme should include:
- Marking points with annotations like M1, A1, B1, DM1, etc.
- Expected answers or solution steps
- Point allocations
Please share the correct content and I'll format it according to your specifications.\begin{enumerate}
\item In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
\end{enumerate}
$$f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } + 5 x + a$$
where $a$ is a constant.\\
Given that ( $2 x - 3$ ) is a factor of $\mathrm { f } ( x )$,\\
(a) use the factor theorem to show that $a = - 3$\\
(b) Hence show that the equation $\mathrm { f } ( x ) = 0$ has only one real root.
\hfill \mbox{\textit{Edexcel P2 2023 Q2 [6]}}