Edexcel C12 2015 January — Question 10

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2015
SessionJanuary
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

10. $$f ( x ) = 6 x ^ { 3 } + a x ^ { 2 } + b x - 5$$ where \(a\) and \(b\) are constants. When \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) there is no remainder.
When \(\mathrm { f } ( x )\) is divided by ( \(2 x - 1\) ) the remainder is - 15
  1. Find the value of \(a\) and the value of \(b\).
  2. Factorise \(\mathrm { f } ( x )\) completely.