6. \(\mathrm { f } ( x ) = k x ^ { 3 } - 15 x ^ { 2 } - 32 x - 12\) where \(k\) is a constant
Given ( \(x - 3\) ) is a factor of \(\mathrm { f } ( x )\),
- show that \(k = 9\)
- Using algebra and showing each step of your working, fully factorise \(\mathrm { f } ( x )\).
- Solve, for \(0 \leqslant \theta < 360 ^ { \circ }\), the equation
$$9 \cos ^ { 3 } \theta - 15 \cos ^ { 2 } \theta - 32 \cos \theta - 12 = 0$$
giving your answers to one decimal place.