CAIE P3 2022 November — Question 2

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionNovember
TopicFactor & Remainder Theorem
TypeSolve inequality involving polynomial

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