Edexcel C2 2014 June — Question 4

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2014
SessionJune
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

4.
\(\mathrm { f } ( x ) = - 4 x ^ { 3 } + a x ^ { 2 } + 9 x - 18\), where \(a\) is a constant. Given that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x )\),
  1. find the value of \(a\),
  2. factorise \(\mathrm { f } ( x )\) completely,
  3. find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(2 x - 1\) ).