5 The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 17 x + 6\).
- Find the remainder when \(\mathrm { f } ( x )\) is divided by \(( x - 3 )\).
- Given that \(\mathrm { f } ( 2 ) = 0\), express \(\mathrm { f } ( x )\) as the product of a linear factor and a quadratic factor.
- Determine the number of real roots of the equation \(\mathrm { f } ( x ) = 0\), giving a reason for your answer.