3 The polynomial \(4 x ^ { 3 } + a x ^ { 2 } + b x - 2\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( x + 1 )\) and \(( x + 2 )\) are factors of \(\mathrm { p } ( x )\).
- Find the values of \(a\) and \(b\).
- When \(a\) and \(b\) have these values, find the remainder when \(\mathrm { p } ( x )\) is divided by \(\left( x ^ { 2 } + 1 \right)\).