| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2011 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Verify factor then simplify rational expression |
| Difficulty | Moderate -0.8 This is a straightforward application of the Factor Theorem with routine algebraic manipulation. Part (a) is direct substitution, part (b) requires evaluating f(3/2) to verify the factor, and part (c) involves factoring both numerator and denominator then canceling common factors. All steps are standard textbook exercises requiring no problem-solving insight, making it easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02k Simplify rational expressions: factorising, cancelling, algebraic division |
1 The polynomial $\mathrm { f } ( x )$ is defined by $\mathrm { f } ( x ) = 4 x ^ { 3 } - 13 x + 6$.
\begin{enumerate}[label=(\alph*)]
\item Find $\mathrm { f } ( - 2 )$.
\item Use the Factor Theorem to show that $2 x - 3$ is a factor of $\mathrm { f } ( x )$.
\item Simplify $\frac { 2 x ^ { 2 } + x - 6 } { \mathrm { f } ( x ) }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2011 Q1 [7]}}