Edexcel P4 2023 January — Question 1

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2023
SessionJanuary
TopicGeneralised Binomial Theorem and Partial Fractions

1. $$f ( x ) = \frac { 5 x + 10 } { ( 1 - x ) ( 2 + 3 x ) }$$
  1. Write \(\mathrm { f } ( x )\) in partial fraction form.
    1. Hence find, in ascending powers of \(x\) up to and including the terms in \(x ^ { 2 }\), the binomial series expansion of \(\mathrm { f } ( x )\). Give each coefficient as a simplified fraction.
    2. Find the range of values of \(x\) for which this expansion is valid.