Edexcel C2 — Question 6

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

6. \(\mathrm { f } ( x ) = 6 x ^ { 3 } + p x ^ { 2 } + q x + 8\), where \(p\) and \(q\) are constants. Given that \(\mathrm { f } ( x )\) is exactly divisible by ( \(2 x - 1\) ), and also that when \(\mathrm { f } ( x )\) is divided by ( \(x - 1\) ) the remainder is - 7 ,
  1. find the value of \(p\) and the value of \(q\).
  2. Hence factorise \(\mathrm { f } ( x )\) completely.