CAIE P2 2009 November — Question 3

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2009
SessionNovember
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

3 The polynomial \(4 x ^ { 3 } - 8 x ^ { 2 } + a x - 3\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that ( \(2 x + 1\) ) is a factor of \(\mathrm { p } ( x )\).
  1. Find the value of \(a\).
  2. When \(a\) has this value, factorise \(\mathrm { p } ( x )\) completely.