Edexcel C2 2009 January — Question 6

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2009
SessionJanuary
TopicFactor & Remainder Theorem
TypePolynomial with equal remainders

6. $$f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + a x + b$$ where \(a\) and \(b\) are constants. The remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) ) is equal to the remainder when \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\).
  1. Find the value of \(a\). Given that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\),
  2. find the value of \(b\).