6 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = 4 x ^ { 3 } + 16 x ^ { 2 } + 9 x - 15$$
- Find the quotient when \(\mathrm { p } ( x )\) is divided by \(( 2 x + 3 )\), and show that the remainder is - 6 .
- Find \(\int \frac { \mathrm { p } ( x ) } { 2 x + 3 } \mathrm {~d} x\).
- Factorise \(\mathrm { p } ( x ) + 6\) completely and hence solve the equation
$$p ( \operatorname { cosec } 2 \theta ) + 6 = 0$$
for \(0 ^ { \circ } < \theta < 135 ^ { \circ }\).