CAIE P2 2020 June — Question 2

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionJune
TopicFactor & Remainder Theorem
TypeTwo factors given

2 The polynomial \(\mathrm { p } ( x )\) is defined by $$\mathrm { p } ( x ) = 6 x ^ { 3 } + a x ^ { 2 } + 9 x + b$$ where \(a\) and \(b\) are constants. It is given that \(( x - 2 )\) and \(( 2 x + 1 )\) are factors of \(\mathrm { p } ( x )\).
Find the values of \(a\) and \(b\).