3.
$$f ( x ) = 2 x ^ { 3 } + a x ^ { 2 } + b x - 6$$
where \(a\) and \(b\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( 2 x - 1 )\) the remainder is - 5 .
When \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\) there is no remainder.
- Find the value of \(a\) and the value of \(b\).
- Factorise \(\mathrm { f } ( x )\) completely.