7.
\(( x - 3 )\) is a common factor of \(\mathrm { f } ( x )\) and \(\mathrm { g } ( x )\) where:
$$\begin{aligned}
& \mathrm { f } ( x ) = 2 x ^ { 3 } - 11 x ^ { 2 } + ( p - 15 ) x + q
& \mathrm {~g} ( x ) = 2 x ^ { 3 } - 17 x ^ { 2 } + p x + 2 q
\end{aligned}$$
- Show that \(3 p + q = 90\) and \(3 p + 2 q = 99\)
Fully justify your answer.
- (ii) Hence find the values of \(p\) and \(q\).
- \(\quad \mathrm { h } ( x ) = \mathrm { f } ( x ) + \mathrm { g } ( x )\)
Using your values of \(p\) and \(q\), fully factorise \(\mathrm { h } ( x )\)