7 The polynomial \(\mathrm { f } ( x )\) is given by \(\mathrm { f } ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } + 11 x - 8\).
- Find the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x + 2\) ).
- Use the factor theorem to show that ( \(2 x - 1\) ) is a factor of \(\mathrm { f } ( x )\).
- Express \(\mathrm { f } ( x )\) as a product of a linear factor and a quadratic factor.
- State the number of real roots of the equation \(\mathrm { f } ( x ) = 0\), giving a reason for your answer.