CAIE P2 2004 November — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2004
SessionNovember
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

4 The cubic polynomial \(2 x ^ { 3 } - 5 x ^ { 2 } + a x + b\) is denoted by \(\mathrm { f } ( x )\). It is given that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x )\), and that when \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) the remainder is - 6 . Find the values of \(a\) and \(b\).