Answer
$(z+7)(z+3)$.
Work Step by Step
The given polynomial is
$=z^2+10z+21$
Standard form is $x^2+bx+c$.
We have $b=10$ and $c=21$.
$b$ and $c$ is positive.
Factor pair of $21$, whose sum is $10$:-
$7,3$
The values of $p$ and $q$ are $7$ and $3$.
Hence, the factor of the polynomial is $(z+p)(z+q)=(z+7)(z+3)$.
Check:-
$=(z+7)(z+3)$
$=z^2+3z+7z+21$
$=z^2+10z+21$
True.
