CAIE P3 2023 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

9 Let \(\mathrm { f } ( x ) = \frac { 17 x ^ { 2 } - 7 x + 16 } { \left( 2 + 3 x ^ { 2 } \right) ( 2 - x ) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence obtain the expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\).
  3. State the set of values of \(x\) for which the expansion in (b) is valid. Give your answer in an exact form.