
\begin{enumerate}
\item $\begin{aligned}[t]
z^3 - 27 & = z^3 - 3^3\\
& = \underline{(z-3)(z^2 + 3z + 9)}.
\end{aligned}$

\item $\begin{aligned}[t]
z^5 - \i & = z^5 - \i^5\\
& = (z-\i)(z^4 + \i z^3 + \i^2 z^2 + \i^3z + \i^4)\\
& =  \underline{(z-\i)(z^4 + \i z^3 - z^2 - \i z + 1)}.
\end{aligned}$

\item $\begin{aligned}[t]
z^4 - 4 & = (z^4 - \big(\sqrt2\big)^4\\
& = \big(z-\sqrt2\big)\big(z^3 + \sqrt2z^2 + (\sqrt2)^2z + (\sqrt2)^3\big)\\
& =  \underline{\big(z-\sqrt2\big)\big( z^3 + \sqrt2z^2 + 2z + 2\sqrt2 \big)}.
\end{aligned}$

\item $\begin{aligned}[t]
z^6 + 64 & = z^6 - (2\i)^6\\
& = (z-2\i)\big(z^5 + 2\i z^4 + (2\i)^2z^3 + (2\i)^3z^2 + (2\i)^4z + (2\i)^5 \big)\\
& =  \underline{(z-2\i)\big(z^5 + 2\i z^4 - 4z^3 -8\i z^2 + 16z + 32\i \big)}.
\end{aligned}$
\end{enumerate}
