8 The polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 7 x + 33\).
- Find the remainder when \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\).
- Show that \(( x - 3 )\) is a factor of \(\mathrm { f } ( x )\).
- Solve the equation \(\mathrm { f } ( x ) = 0\), giving each root in an exact form as simply as possible.
On its first trip between Malby and Grenlish, a steam train uses 1.5 tonnes of coal. As the train does more trips, it becomes less efficient so that each subsequent trip uses \(2 \%\) more coal than the previous trip.