6.
$$f ( x ) = - 6 x ^ { 3 } - 7 x ^ { 2 } + 40 x + 21$$
- Use the factor theorem to show that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\)
- Factorise f(x) completely.
- Hence solve the equation
$$6 \left( 2 ^ { 3 y } \right) + 7 \left( 2 ^ { 2 y } \right) = 40 \left( 2 ^ { y } \right) + 21$$
giving your answer to 2 decimal places.