Answer
$(5z^{2}+1)(9z+4)$
Work Step by Step
$45z^{3}+20z^{2}+9z+4=$
...factor by grouping- pair up the first with the third term and the second with the last.
$=9z(5z^{2}+1)+4(5z^{2}+1)$
...use the Distributive Property.
$=(5z^{2}+1)(9z+4)$