Partial fractions with specific coefficient

A question is this type if and only if it asks to find partial fractions and then find only a specific coefficient (e.g., coefficient of x³) in the expansion rather than the full series.

1 questions · Standard +0.8

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CAIE P3 2024 November Q7
9 marks Standard +0.8
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. \includegraphics[max width=\textwidth, alt={}, center]{656df2a8-fc4d-49f3-a649-746103b4576e-13_2726_34_97_21}
  2. Hence find the coefficient of \(x ^ { 3 }\) in the expansion of \(\mathrm { f } ( x )\).