Edexcel C12 2018 January — Question 6

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2018
SessionJanuary
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

6. $$f ( x ) = a x ^ { 3 } - 8 x ^ { 2 } + b x + 6$$ 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 \(( x - 2 )\) the remainder is - 12
  1. Find the value of \(a\) and the value of \(b\).
  2. Factorise \(\mathrm { f } ( x )\) completely.