The polynomial \(p(z)\) is defined by

\(p(z) = z^3 + mz^2 + 24z + 32\),

where \(m\) is a constant. It is given that \((z + 2)\) is a factor of \(p(z)\).

1. Find the value of \(m\).
2. Hence, showing all your working, find
   1. the three roots of the equation \(p(z) = 0\),
   2. the six roots of the equation \(p(z^2) = 0\).