6 The polynomial \(\mathrm { p } ( x )\) is given by \(\mathrm { p } ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x\).
- Use the Factor Theorem to show that \(x - 3\) is a factor of \(\mathrm { p } ( x )\).
- Express \(\mathrm { p } ( x )\) as the product of three linear factors.
- Use the Remainder Theorem to find the remainder, \(r\), when \(\mathrm { p } ( x )\) is divided by \(x - 2\).
- Using algebraic division, or otherwise, express \(\mathrm { p } ( x )\) in the form
$$( x - 2 ) \left( x ^ { 2 } + a x + b \right) + r$$
where \(a , b\) and \(r\) are constants.