5 The polynomial \(\mathrm { p } ( x )\) is given by
$$\mathrm { p } ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 3 x + 18$$
- Use the Remainder Theorem to find the remainder when \(\mathrm { p } ( x )\) is divided by \(x + 1\).
- Use the Factor Theorem to show that \(x - 3\) is a factor of \(\mathrm { p } ( x )\).
- Express \(\mathrm { p } ( x )\) as a product of linear factors.
- Sketch the curve with equation \(y = x ^ { 3 } - 4 x ^ { 2 } - 3 x + 18\), stating the values of \(x\) where the curve meets the \(x\)-axis.