| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Type | Simple Algebraic Fraction Simplification |
| Difficulty | Moderate -0.3 This is a standard C4 polynomial question requiring routine application of the Factor Theorem, polynomial division, and algebraic fraction simplification. While multi-part, each step follows predictable textbook methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02k Simplify rational expressions: factorising, cancelling, algebraic division |
1
\begin{enumerate}[label=(\alph*)]
\item The polynomial $\mathrm { p } ( x )$ is defined by $\mathrm { p } ( x ) = 6 x ^ { 3 } - 19 x ^ { 2 } + 9 x + 10$.
\begin{enumerate}[label=(\roman*)]
\item Find $\mathrm { p } ( 2 )$.
\item Use the Factor Theorem to show that ( $2 x + 1$ ) is a factor of $\mathrm { p } ( x )$.
\item Write $\mathrm { p } ( x )$ as the product of three linear factors.
\end{enumerate}\item Hence simplify $\frac { 3 x ^ { 2 } - 6 x } { 6 x ^ { 3 } - 19 x ^ { 2 } + 9 x + 10 }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2006 Q1 [8]}}