CAIE P3 2024 November — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2024
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

7
Let \(f ( x ) = \frac { 5 x ^ { 2 } + 8 x + 5 } { ( 1 + 2 x ) \left( 2 + x ^ { 2 } \right) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
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  2. Hence find the coefficient of \(x ^ { 3 }\) in the expansion of \(\mathrm { f } ( x )\).