3.
$$f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + a x + 18$$
where \(a\) is a constant.
Given that \(( x - 3 )\) is a factor of \(\mathrm { f } ( x )\),
- show that \(a = - 9\)
- factorise \(\mathrm { f } ( x )\) completely.
Given that
$$\mathrm { g } ( y ) = 2 \left( 3 ^ { 3 y } \right) - 5 \left( 3 ^ { 2 y } \right) - 9 \left( 3 ^ { y } \right) + 18$$
- find the values of \(y\) that satisfy \(\mathrm { g } ( y ) = 0\), giving your answers to 2 decimal places where appropriate.