11 You are given that \(\mathrm { f } ( x ) = ( 2 x - 3 ) ( x + 2 ) ( x + 4 )\).
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- State the roots of \(\mathrm { f } ( x - 2 ) = 0\).
- You are also given that \(\mathrm { g } ( x ) = \mathrm { f } ( x ) + 15\).
(A) Show that \(\mathrm { g } ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 2 x - 9\).
(B) Show that \(\mathrm { g } ( 1 ) = 0\) and hence factorise \(\mathrm { g } ( x )\) completely.