5 The cubic polynomial \(\mathrm { f } ( x )\) is given by
$$f ( x ) = x ^ { 3 } + a x + b$$
where \(a\) and \(b\) are constants. It is given that ( \(x + 1\) ) is a factor of \(\mathrm { f } ( x )\) and that the remainder when \(\mathrm { f } ( x )\) is divided by \(( x - 3 )\) is 16 .
- Find the values of \(a\) and \(b\).
- Hence verify that \(\mathrm { f } ( 2 ) = 0\), and factorise \(\mathrm { f } ( x )\) completely.