Edexcel C4 2017 June — Question 2

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2017
SessionJune
TopicGeneralised Binomial Theorem
TypeFinding unknown power and constant

2. \(\quad \mathrm { f } ( x ) = ( 2 + k x ) ^ { - 3 } , \quad | k x | < 2\), where \(k\) is a positive constant The binomial expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\) is $$A + B x + \frac { 243 } { 16 } x ^ { 2 }$$ where \(A\) and \(B\) are constants.
  1. Write down the value of \(A\).
  2. Find the value of \(k\).
  3. Find the value of \(B\).