Answer
$(z+3)(z^2+7)$
Work Step by Step
Using factoring by grouping, the factored form of the given expression, $
z^3+3z^2+7z+21
,$ is
\begin{array}{l}
(z^3+3z^2)+(7z+21)
\\\\=
z^2(z+3)+7(z+3)
\\\\=
(z+3)(z^2+7)
.\end{array}
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