Edexcel C2 2006 January — Question 1

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2006
SessionJanuary
TopicFactor & Remainder Theorem
TypeGiven factor, find all roots
  1. \(\mathrm { f } ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 5 x + c\), where \(c\) is a constant.
Given that \(\mathrm { f } ( 1 ) = 0\),
  1. find the value of \(c\),
  2. factorise \(\mathrm { f } ( x )\) completely,
  3. find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(2 x - 3\) ).
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