CAIE P3 2019 November — Question 2

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionNovember
TopicFactor & Remainder Theorem
TypeOne factor, one non-zero remainder

2 The polynomial \(6 x ^ { 3 } + a x ^ { 2 } + b x - 2\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( 2 x + 1 )\) is a factor of \(\mathrm { p } ( x )\) and that when \(\mathrm { p } ( x )\) is divided by \(( x + 2 )\) the remainder is - 24 . Find the values of \(a\) and \(b\).