Unknown complex roots of a real quintic from the sum and product of its roots, then its quadratic factors

The polynomial \(p(z)=2z^5-3z^4+cz^3+dz^2+ez+40\) has real coefficients \(c\), \(d\) and \(e\), and \(z\in\mathbb{C}\).

The equation \(p(z)=0\) has \(-\frac12\), \(m+2i\) and \(-1+ni\) among its roots, where \(m\) and \(n\) are real and \(n>0\).

1. By forming the sum of all five roots and their product,
   1. show that \(m=2\);
   2. find \(n\).[5]
2. Hence express \(p(z)\) as the product of a linear factor and two quadratic factors, each with integer coefficients.[3]