4 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = 6 x ^ { 3 } + 11 x ^ { 2 } + a x + a$$
where \(a\) is a constant. It is given that \(( x + 2 )\) is a factor of \(\mathrm { p } ( x )\).
- Use the factor theorem to show that \(a = - 4\).
- When \(a = - 4\),
(a) factorise \(\mathrm { p } ( x )\) completely,
(b) solve the equation \(6 \sec ^ { 3 } \theta + 11 \sec ^ { 2 } \theta + a \sec \theta + a = 0\) for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).