7.
$$g ( x ) = 2 x ^ { 3 } + a x ^ { 2 } - 18 x - 8$$
Given that \(( x + 2 )\) is a factor of \(\mathrm { g } ( x )\),
- show that \(a = - 3\)
- Hence, using algebra, fully factorise \(\mathrm { g } ( x )\).
Using your answer to part (b),
- solve, for \(0 \leqslant \theta < 2 \pi\), the equation
$$2 \sin ^ { 3 } \theta - 3 \sin ^ { 2 } \theta - 18 \sin \theta = 8$$
giving each answer, in radians, as a multiple of \(\pi\).