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 \(\mathrm { f } ( x )\).
- Find the value of \(a\).
- Find all the factors of \(\mathrm { f } ( x )\).