CAIE P3 2014 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2014
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

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