| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Two unknowns with show-that step |
| Difficulty | Moderate -0.5 This is a straightforward application of the Remainder Theorem requiring students to substitute x=1 and x=-2, set up two simultaneous equations, and solve. The 'show that' in part (a) guides students through the process, making it easier than average for A-level but still requiring correct algebraic manipulation. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
6.
$$\mathrm { f } ( x ) = x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + a x + b ,$$
where $a$ and $b$ are constants.
When $\mathrm { f } ( x )$ is divided by $( x - 1 )$, the remainder is 7
\begin{enumerate}[label=(\alph*)]
\item Show that $a + b = 3$
When $\mathrm { f } ( x )$ is divided by ( $x + 2$ ), the remainder is - 8
\item Find the value of $a$ and the value of $b$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q6 [7]}}