The polynomial \(x ^ { 4 } + a x ^ { 3 } - x ^ { 2 } + b x + 2\), 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 quotient when \(\mathrm { p } ( x )\) is divided by \(x ^ { 2 } + x - 2\).