5.
$$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12$$
- Using the factor theorem, explain why \(\mathrm { f } ( x )\) is divisible by \(( x + 3 )\).
- Hence fully factorise \(\mathrm { f } ( x )\).
- Show that \(\frac { x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12 } { x ^ { 3 } + 5 x ^ { 2 } + 6 x }\) can be written in the form \(A + \frac { B } { x }\) where \(A\) and \(B\) are integers to be found.