8.
$$f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } - 23 x - 10$$
- Find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 3\) ).
- Show that ( \(x + 2\) ) is a factor of \(\mathrm { f } ( x )\).
- Hence fully factorise \(\mathrm { f } ( x )\).
- Hence solve
$$2 \left( 3 ^ { 3 t } \right) - 5 \left( 3 ^ { 2 t } \right) - 23 \left( 3 ^ { t } \right) = 10$$
giving your answer to 3 decimal places.