If you multiplied out:
then how would you form each coefficient so as to make the left hand side look like the right hand side? Note:
Viewed in this way, you are looking at a problem in combinations and permutations.
Show that if the polynomial p(z) = a_{n}z^{n}+a_{n-1}z^{n-1}+…+a_{0} is written in factored form as p(z) = a_{n}(z-z_{1})^{d1}(z-z_{2})^{d2}…(z-z_{r})^{dr}, then
(a) n = d_{1}+d_{2}+…+d_{r}
(b) a_{n-1} = -a_{n}(d_{1}z_{1}+d_{2}z_{2}+…d_{r}z_{r})
(c) a_{0} = a_{n}(-1)^{n}z_{1}^{d1}z_{2}^{d2}…z_{r}^{dr}