OCR PURE — Question 2

Exam BoardOCR
ModulePURE
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

2 In this question you must show detailed reasoning.
The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 5 x ^ { 3 } - 4 x ^ { 2 } + a x - 2\), where \(a\) is a constant. You are given that \(( x - 2 )\) is a factor of \(\mathrm { f } ( x )\).
  1. Find the value of \(a\).
  2. Find all the factors of \(\mathrm { f } ( x )\).