CAIE P2 2011 June — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2011
SessionJune
TopicPolynomial Division & Manipulation

4 The polynomial \(\mathrm { f } ( x )\) is defined by $$f ( x ) = 3 x ^ { 3 } + a x ^ { 2 } + a x + a$$ where \(a\) is a constant.
  1. Given that \(( x + 2 )\) is a factor of \(\mathrm { f } ( x )\), find the value of \(a\).
  2. When \(a\) has the value found in part (i), find the quotient when \(\mathrm { f } ( x )\) is divided by ( \(x + 2\) ).