Answer
$z^{3}-5z^{2}+13z-9$
Work Step by Step
$\begin{array}{lllllllll}
& z^{2} & -4z & +9 & & & & & \\
& & z & -1 & & & & & \\
-- & -- & -- & -- & & & & & \\
& -z^{2} & +4z & -9 & \text{multiply by }-1 & & & & \\
z^{3} & -4z^{2} & +9z & & \text{multiply by }z & & & & \\
-- & -- & -- & -- & \text{add like terms } & & & & \\
z^{3} & -5z^{2} & +13z & -9 & & & & &
\end{array}$
Answer: $z^{3}-5z^{2}+13z-9$
