7.
$$f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + x + 2$$
- Show that \(( x - 2 )\) is a factor of \(\mathrm { f } ( x )\).
- Fully factorise \(\mathrm { f } ( x )\).
- Solve the equation \(\mathrm { f } ( x ) = 0\).
- Find the values of \(\theta\) in the interval \(0 \leq \theta \leq 2 \pi\) for which
$$2 \sin ^ { 3 } \theta - 5 \sin ^ { 2 } \theta + \sin \theta + 2 = 0$$
giving your answers in terms of \(\pi\).