(a)[3]
Determine the quotient obtained when $p(x)$ is divided by $(2x + 3)$, and verify that the remainder equals $-6$.
(b)[2]
Evaluate $\int \frac{p(x)}{2x + 3}\,dx$.
(c)[5]
Factorise $p(x) + 6$ fully, and so solve $p(\cosec 2\theta) + 6 = 0$ for $0^\circ < \theta < 135^\circ$.