Edexcel C2 2014 January — Question 2

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2014
SessionJanuary
TopicFactor & Remainder Theorem
TypeOne factor, one non-zero remainder

2. \(\mathrm { f } ( x ) = 2 x ^ { 3 } + x ^ { 2 } + a x + b\), where \(a\) and \(b\) are constants. Given that when \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) ) the remainder is 25 ,
  1. show that \(2 a + b = 5\) Given also that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\),
  2. find the value of \(a\) and the value of \(b\).
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