9.
$$f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 24 x - 16 .$$
- Evaluate \(\mathrm { f } ( 1 )\) and hence state a linear factor of \(\mathrm { f } ( x )\).
- Show that \(\mathrm { f } ( x )\) can be expressed in the form
$$\mathrm { f } ( x ) = ( x + p ) ( x + q ) ^ { 2 } ,$$
where \(p\) and \(q\) are integers to be found.
- Sketch the curve \(y = \mathrm { f } ( x )\).
- Using integration, find the area of the region enclosed by the curve \(y = \mathrm { f } ( x )\) and the \(x\)-axis.