CAIE P2 2003 November — Question 3

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2003
SessionNovember
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

3 The polynomial \(x ^ { 4 } - 6 x ^ { 2 } + x + a\) is denoted by \(\mathrm { f } ( x )\).
  1. It is given that \(( x + 1 )\) is a factor of \(\mathrm { f } ( x )\). Find the value of \(a\).
  2. When \(a\) has this value, verify that ( \(x - 2\) ) is also a factor of \(\mathrm { f } ( x )\) and hence factorise \(\mathrm { f } ( x )\) completely.