5 The polynomial \(\mathrm { p } ( x )\) is given by \(\mathrm { p } ( x ) = x ^ { 3 } + c x ^ { 2 } + d x - 12\), where \(c\) and \(d\) are constants.
- When \(\mathrm { p } ( x )\) is divided by \(x + 2\), the remainder is - 150 .
Show that \(2 c - d + 65 = 0\).
- Given that \(x - 3\) is a factor of \(\mathrm { p } ( x )\), find another equation involving \(c\) and \(d\).
- By solving these two equations, find the value of \(c\) and the value of \(d\).