3.
$$f ( x ) = 6 x ^ { 3 } + 17 x ^ { 2 } + 4 x - 12$$
- Use the factor theorem to show that ( \(2 x + 3\) ) is a factor of \(\mathrm { f } ( x )\).
- Hence, using algebra, write \(\mathrm { f } ( x )\) as a product of three linear factors.
- Solve, for \(\frac { \pi } { 2 } < \theta < \pi\), the equation
$$6 \tan ^ { 3 } \theta + 17 \tan ^ { 2 } \theta + 4 \tan \theta - 12 = 0$$
giving your answers to 3 significant figures.