CAIE P3 2020 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

9 Let \(\mathrm { f } ( x ) = \frac { 8 + 5 x + 12 x ^ { 2 } } { ( 1 - x ) ( 2 + 3 x ) ^ { 2 } }\).
  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 \(x ^ { 2 }\).