1 You are given that \(\mathrm { f } ( x ) = x ^ { 3 } + 6 x ^ { 2 } - x - 30\).
- Use the factor theorem to find a root of \(\mathrm { f } ( x ) = 0\) and hence factorise \(\mathrm { f } ( x )\) completely.
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- The graph of \(y = \mathrm { f } ( x )\) is translated by \(\binom { 1 } { 0 }\).
Show that the equation of the translated graph may be written as
$$y = x ^ { 3 } + 3 x ^ { 2 } - 10 x - 24$$