CAIE P3 2022 June — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJune
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

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