CAIE P3 2017 March — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionMarch
TopicGeneralised Binomial Theorem and Partial Fractions

9 Let \(\mathrm { f } ( x ) = \frac { x ( 6 - x ) } { ( 2 + x ) \left( 4 + x ^ { 2 } \right) }\).
  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 \(x ^ { 2 }\).