3. \(\mathrm { f } ( x ) = 6 x ^ { 3 } + 3 x ^ { 2 } + A x + B\), where \(A\) and \(B\) are constants.
Given that when \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) the remainder is 45 ,
- show that \(B - A = 48\)
Given also that ( \(2 x + 1\) ) is a factor of \(\mathrm { f } ( x )\),
- find the value of \(A\) and the value of \(B\).
- Factorise f(x) fully.