CAIE P3 2013 November — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2013
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

7 Let \(\mathrm { f } ( x ) = \frac { 2 x ^ { 2 } - 7 x - 1 } { ( x - 2 ) \left( x ^ { 2 } + 3 \right) }\).
  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 \(x ^ { 2 }\).