CAIE P3 2021 March — Question 2

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionMarch
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

2 The polynomial \(a x ^ { 3 } + 5 x ^ { 2 } - 4 x + b\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( x + 2 )\) is a factor of \(\mathrm { p } ( x )\) and that when \(\mathrm { p } ( x )\) is divided by \(( x + 1 )\) the remainder is 2 . Find the values of \(a\) and \(b\).