1 The polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 27 x ^ { 3 } - 9 x + 2\).
- Find the remainder when \(\mathrm { f } ( x )\) is divided by \(3 x + 1\).
- Show that f \(\left( - \frac { 2 } { 3 } \right) = 0\).
- Express \(\mathrm { f } ( x )\) as a product of three linear factors.
- Simplify
$$\frac { 27 x ^ { 3 } - 9 x + 2 } { 9 x ^ { 2 } + 3 x - 2 }$$