The polynomial \(2 x ^ { 3 } + a x ^ { 2 } - a x - 12\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that \(( x + 1 )\) is a factor of \(\mathrm { p } ( x )\). Find the value of \(a\).
When \(a\) has this value, find the remainder when \(\mathrm { p } ( x )\) is divided by \(( x + 3 )\).