| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single polynomial, two remainder/factor conditions |
| Difficulty | Moderate -0.5 This is a straightforward application of the Remainder Theorem requiring students to substitute two values, set up simultaneous equations, and solve for constants a and b, followed by verification that f(2)=0. While it involves multiple steps and simultaneous equations, it's a standard textbook exercise with no novel insight required—slightly easier than the average A-level question due to its routine nature. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
2. $\mathrm { f } ( x ) = x ^ { 3 } + a x ^ { 2 } + b x - 10$, where $a$ and $b$ are constants. When $\mathrm { f } ( x )$ is divided by $( x - 3 )$, the remainder is 14 . When $\mathrm { f } ( x )$ is divided by $( x + 1 )$, the remainder is - 18 .
\begin{enumerate}[label=(\alph*)]
\item Find the value of $a$ and the value of $b$.
\item Show that $( x - 2 )$ is a factor of $\mathrm { f } ( x )$.\\[0pt]
[P3 June 2002 Question 1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q2 [7]}}