Edexcel C2 2015 June — Question 3

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2015
SessionJune
TopicFactor & Remainder Theorem
TypeTwo unknowns with show-that step

3. \(\mathrm { f } ( x ) = 6 x ^ { 3 } + 3 x ^ { 2 } + A x + B\), where \(A\) and \(B\) are constants. Given that when \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) the remainder is 45 ,
  1. show that \(B - A = 48\) Given also that ( \(2 x + 1\) ) is a factor of \(\mathrm { f } ( x )\),
  2. find the value of \(A\) and the value of \(B\).
  3. Factorise f(x) fully.