10.
$$f ( x ) = 6 x ^ { 3 } + a x ^ { 2 } + b x - 5$$
where \(a\) and \(b\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) there is no remainder.
When \(\mathrm { f } ( x )\) is divided by ( \(2 x - 1\) ) the remainder is - 15
- Find the value of \(a\) and the value of \(b\).
- Factorise \(\mathrm { f } ( x )\) completely.