CAIE P3 2004 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2004
SessionNovember
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

3 The polynomial \(2 x ^ { 3 } + a x ^ { 2 } - 4\) is denoted by \(\mathrm { p } ( x )\). It is given that ( \(x - 2\) ) is a factor of \(\mathrm { p } ( x )\).
  1. Find the value of \(a\). When \(a\) has this value,
  2. factorise \(\mathrm { p } ( x )\),
  3. solve the inequality \(\mathrm { p } ( x ) > 0\), justifying your answer.