3 The polynomial \(\mathrm { p } ( x )\) is given by
$$\mathrm { p } ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6$$
- Use the Factor Theorem to show that \(x + 1\) is a factor of \(\mathrm { p } ( x )\).
- Express \(\mathrm { p } ( x )\) as the product of three linear factors.
- Verify that \(\mathrm { p } ( 0 ) > \mathrm { p } ( 1 )\).
- Sketch the curve with equation \(y = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6\), indicating the values where the curve crosses the \(x\)-axis.