6 The polynomial \(\mathrm { p } ( x )\) is given by
$$\mathrm { p } ( x ) = x ^ { 3 } + x ^ { 2 } - 10 x + 8$$
- Using the factor theorem, show that \(x - 2\) is a factor of \(\mathrm { p } ( x )\).
- Hence express \(\mathrm { p } ( x )\) as the product of three linear factors.
- Sketch the curve with equation \(y = x ^ { 3 } + x ^ { 2 } - 10 x + 8\), showing the coordinates of the points where the curve cuts the axes.
(You are not required to calculate the coordinates of the stationary points.)