Edexcel C2 2013 June — Question 4

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2013
SessionJune
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

4. \(\mathrm { f } ( x ) = a x ^ { 3 } - 11 x ^ { 2 } + b x + 4\), where \(a\) and \(b\) are constants. When \(\mathrm { f } ( x )\) is divided by ( \(x - 3\) ) the remainder is 55
When \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) the remainder is - 9
  1. Find the value of \(a\) and the value of \(b\). Given that \(( 3 x + 2 )\) is a factor of \(\mathrm { f } ( x )\),
  2. factorise \(\mathrm { f } ( x )\) completely.