| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Polynomial with equal remainders |
| Difficulty | Moderate -0.8 This is a straightforward application of the Remainder Theorem requiring students to evaluate f(1) and f(-1/2), set them equal, and solve for p. The algebra is routine with no conceptual challenges beyond knowing the theorem itself, making it easier than average for A-level. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
f(x) = px³ + 6x² + 12x + q.
Given that the remainder when f(x) is divided by (x - 1) is equal to the remainder when f(x) is divided by (2x + 1),
\begin{enumerate}[label=(\alph*)]
\item find the value of p. [4]
\end{enumerate}
Given also that q = 3, and p has the value found in part (a),
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of the remainder. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q1 [5]}}