8.
$$f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 5 x + 12$$
- Show that
$$( x + 1 ) ( x - 3 ) ( x - 4 ) \equiv x ^ { 3 } - 6 x ^ { 2 } + 5 x + 12$$
- Sketch the curve \(y = \mathrm { f } ( x )\), showing the coordinates of any points of intersection with the coordinate axes.
- Showing the coordinates of any points of intersection with the coordinate axes, sketch on separate diagrams the curves
- \(\quad y = \mathrm { f } ( x + 3 )\),
- \(y = \mathrm { f } ( - x )\).