4 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = a x ^ { 3 } + 23 x ^ { 2 } - a x - 8$$
where \(a\) is a constant. It is given that \(( 2 x + 1 )\) is a factor of \(\mathrm { p } ( x )\).
- Find the value of \(a\) and hence factorise \(\mathrm { p } ( x )\) completely.
- Hence solve the equation \(\mathrm { p } \left( \mathrm { e } ^ { 4 y } \right) = 0\), giving your answer correct to 3 significant figures.