7 The polynomial \(2 x ^ { 3 } - 4 x ^ { 2 } + a x + b\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that when \(\mathrm { p } ( x )\) is divided by \(( x + 1 )\) the remainder is 4 , and that when \(\mathrm { p } ( x )\) is divided by \(( x - 3 )\) the remainder is 12 .

1. Find the values of \(a\) and \(b\).
2. When \(a\) and \(b\) have these values, find the quotient and remainder when \(\mathrm { p } ( x )\) is divided by ( \(x ^ { 2 } - 2\) ).