5 The polynomial \(a x ^ { 3 } + b x ^ { 2 } + 5 x - 2\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( 2 x - 1 )\) is a factor of \(\mathrm { p } ( x )\) and that when \(\mathrm { p } ( x )\) is divided by \(( x - 2 )\) the remainder is 12 .
- Find the values of \(a\) and \(b\).
- When \(a\) and \(b\) have these values, find the quadratic factor of \(\mathrm { p } ( x )\).