CAIE P3 2019 March — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionMarch
TopicGeneralised Binomial Theorem and Partial Fractions

8 Let \(\mathrm { f } ( x ) = \frac { 12 + 12 x - 4 x ^ { 2 } } { ( 2 + x ) ( 3 - 2 x ) }\).
  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 \(x ^ { 2 }\).