6. The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = 2 x ^ { 3 } + x ^ { 2 } + a x + b ,$$
where \(a\) and \(b\) are constants.
Given that when \(\mathrm { p } ( x )\) is divided by \(( x + 2 )\) there is a remainder of 20 ,
- find an expression for \(b\) in terms of \(a\).
Given also that \(( x + 3 )\) is a factor of \(\mathrm { p } ( x )\),
- find the values of \(a\) and \(b\),
- fully factorise \(\mathrm { p } ( x )\).