CAIE P3 2003 June — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2003
SessionJune
TopicFactor & Remainder Theorem
TypeFind constants with divisibility condition

4 The polynomial \(x ^ { 4 } - 2 x ^ { 3 } - 2 x ^ { 2 } + a\) is denoted by \(\mathrm { f } ( x )\). It is given that \(\mathrm { f } ( x )\) is divisible by \(x ^ { 2 } - 4 x + 4\).
  1. Find the value of \(a\).
  2. When \(a\) has this value, show that \(\mathrm { f } ( x )\) is never negative.