4.
$$f ( x ) = x ^ { 3 } + x ^ { 2 } + 44 x + 150$$
Given that \(\mathrm { f } ( x ) = ( x + 3 ) \left( x ^ { 2 } + a x + b \right)\), where \(a\) and \(b\) are real constants,
- find the value of \(a\) and the value of \(b\).
- Find the three roots of \(\mathrm { f } ( x ) = 0\).
- Find the sum of the three roots of \(\mathrm { f } ( x ) = 0\).