4 In this question you must show detailed reasoning.
The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 11 x + 6\).
- Use the factor theorem to show that \(( 2 x - 1 )\) is a factor of \(\mathrm { f } ( x )\).
- Express \(\mathrm { f } ( x )\) in fully factorised form.
- Hence solve the equation \(2 \times 8 ^ { y } - 3 \times 4 ^ { y } - 11 \times 2 ^ { y } + 6 = 0\).