Edexcel C2 2005 January — Question 5

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

  1. \(\quad \mathrm { f } ( x ) = x ^ { 3 } - 2 x ^ { 2 } + a x + b\), where \(a\) and \(b\) are constants.
When \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) ), the remainder is 1 .
When \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\), the remainder is 28 .
  1. Find the value of \(a\) and the value of \(b\).
  2. Show that ( \(x - 3\) ) is a factor of \(\mathrm { f } ( x )\).