4 The polynomial \(a x ^ { 3 } - 20 x ^ { 2 } + x + 3\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that \(( 3 x + 1 )\) is a factor of \(\mathrm { p } ( x )\).
- Find the value of \(a\).
- When \(a\) has this value, factorise \(\mathrm { p } ( x )\) completely.