8.
$$f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + p x + q$$
where \(p\) and \(q\) are constants.
When \(\mathrm { f } ( x )\) is divided by \(( x - 1 )\), the remainder is - 6
- Use the remainder theorem to show that \(p + q = - 5\)
Given also that \(( x + 2 )\) is a factor of \(\mathrm { f } ( x )\),
- find the value of \(p\) and the value of \(q\).
- Factorise \(\mathrm { f } ( \mathrm { x } )\) completely.