CAIE P3 2023 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

3 The polynomial \(2 x ^ { 3 } + a x ^ { 2 } - 11 x + b\) 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 \(( x + 1 )\) the remainder is 12 . Find the values of \(a\) and \(b\).