4 The polynomial \(4 x ^ { 3 } + a x + 2\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that ( \(2 x + 1\) ) is a factor of \(\mathrm { p } ( x )\).
- Find the value of \(a\).
- When \(a\) has this value,
(a) factorise \(\mathrm { p } ( x )\),
(b) solve the inequality \(\mathrm { p } ( x ) > 0\), justifying your answer.