3 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = a x ^ { 3 } - 3 x ^ { 2 } - 5 x + a + 4 ,$$
where \(a\) is a constant.
- Given that \(( x - 2 )\) is a factor of \(\mathrm { p } ( x )\), find the value of \(a\).
- When \(a\) has this value,
(a) factorise \(\mathrm { p } ( x )\) completely,
(b) find the remainder when \(\mathrm { p } ( x )\) is divided by \(( x + 1 )\).