5 The polynomial \(\mathrm { p } ( x )\) is given by
$$\mathrm { p } ( x ) = x ^ { 3 } + c x ^ { 2 } + d x + 3$$
where \(c\) and \(d\) are integers.
- Given that \(x + 3\) is a factor of \(\mathrm { p } ( x )\), show that
$$3 c - d = 8$$
- The remainder when \(\mathrm { p } ( x )\) is divided by \(x - 2\) is 65 .
Obtain a further equation in \(c\) and \(d\).
- Use the equations from parts (a) and (b) to find the value of \(c\) and the value of \(d\). [3 marks]