OCR C2 2010 June — Question 1

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2010
SessionJune
TopicFactor & Remainder Theorem
TypeSingle unknown constant

1 The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = x ^ { 3 } + a x ^ { 2 } - a x - 14\), where \(a\) is a constant.
  1. Given that \(( x - 2 )\) is a factor of \(\mathrm { f } ( x )\), find the value of \(a\).
  2. Using this value of \(a\), find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x + 1\) ).