CAIE P3 2013 June — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2013
SessionJune
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

4 The polynomial \(a x ^ { 3 } - 20 x ^ { 2 } + x + 3\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that \(( 3 x + 1 )\) is a factor of \(\mathrm { p } ( x )\).
  1. Find the value of \(a\).
  2. When \(a\) has this value, factorise \(\mathrm { p } ( x )\) completely.