4 You are given that \(\mathrm { f } ( x ) = 2 x ^ { 3 } + 7 x ^ { 2 } - 7 x - 12\).
- Verify that \(x = - 4\) is a root of \(\mathrm { f } ( x ) = 0\).
- Hence express \(\mathrm { f } ( x )\) in fully factorised form.
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Show that \(\mathrm { f } ( x - 4 ) = 2 x ^ { 3 } - 17 x ^ { 2 } + 33 x\).