9 The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 4 x ^ { 3 } - 7 x - 3\).
- Find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) ).
- Show that ( \(2 x + 1\) ) is a factor of \(\mathrm { f } ( x )\) and hence factorise \(\mathrm { f } ( x )\) completely.
- Solve the equation
$$4 \cos ^ { 3 } \theta - 7 \cos \theta - 3 = 0$$
for \(0 \leqslant \theta \leqslant 2 \pi\). Give each solution for \(\theta\) in an exact form.