10 The polynomial \(x ^ { 3 } + 5 x ^ { 2 } + 31 x + 75\) is denoted by \(\mathrm { p } ( x )\).
- Show that \(( x + 3 )\) is a factor of \(\mathrm { p } ( x )\).
- Show that \(z = - 1 + 2 \sqrt { 6 } \mathrm { i }\) is a root of \(\mathrm { p } ( z ) = 0\).
- Hence find the complex numbers \(z\) which are roots of \(\mathrm { p } \left( z ^ { 2 } \right) = 0\).
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.