OCR C2 2006 June — Question 8

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
TopicFactor & Remainder Theorem
TypeSingle polynomial, two remainder/factor conditions

8 The cubic polynomial \(2 x ^ { 3 } + a x ^ { 2 } + b x - 10\) is denoted by \(\mathrm { f } ( x )\). It is given that, when \(\mathrm { f } ( x )\) is divided by \(( x - 2 )\), the remainder is 12 . It is also given that ( \(x + 1\) ) is a factor of \(\mathrm { f } ( x )\).
  1. Find the values of \(a\) and \(b\).
  2. Divide \(\mathrm { f } ( x )\) by ( \(x + 2\) ) to find the quotient and the remainder.