3 You are given that \(\mathrm { f } ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 20 x + 12\).
- Show that \(x = - 2\) is a root of \(\mathrm { f } ( x ) = 0\).
- Divide \(\mathrm { f } ( x )\) by \(x + 6\).
- Express \(\mathrm { f } ( x )\) in fully factorised form.
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Solve the equation \(\mathrm { f } ( x ) = 12\).