CAIE P3 2007 June — Question 2

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2007
SessionJune
TopicFactor & Remainder Theorem
TypeSingle unknown constant

2 The polynomial \(x ^ { 3 } - 2 x + a\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that ( \(x + 2\) ) is a factor of \(\mathrm { p } ( x )\).
  1. Find the value of \(a\).
  2. When \(a\) has this value, find the quadratic factor of \(\mathrm { p } ( x )\).