6.
$$f ( x ) = a x ^ { 3 } - 8 x ^ { 2 } + b x + 6$$
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 \(( x - 2 )\) the remainder is - 12
- Find the value of \(a\) and the value of \(b\).
- Factorise \(\mathrm { f } ( x )\) completely.