7 The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 12 - 22 x + 9 x ^ { 2 } - x ^ { 3 }\).
- Find the remainder when \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\).
- Show that ( \(3 - x\) ) is a factor of \(\mathrm { f } ( x )\).
- Express \(\mathrm { f } ( x )\) as the product of a linear factor and a quadratic factor.
- Hence solve the equation \(\mathrm { f } ( x ) = 0\), giving each root in simplified surd form where appropriate.