7 The polynomial \(\mathrm { p } ( x )\) is defined by
$$p ( x ) = 9 x ^ { 3 } + 6 x ^ { 2 } + 12 x + k$$
where \(k\) is a constant.
- Find the quotient when \(\mathrm { p } ( x )\) is divided by \(( 3 x + 2 )\) and show that the remainder is \(( k - 8 )\).
- It is given that \(\int _ { 1 } ^ { 6 } \frac { \mathrm { p } ( \mathrm { x } ) } { 3 \mathrm { x } + 2 } \mathrm { dx } = \mathrm { a } + \ln 64\), where \(a\) is an integer.
Find the values of \(a\) and \(k\).
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