Answer
$3z(z^{2}-2z+3)$
Work Step by Step
Original Expression : $3z^{3}-6z^{2}+9z$
Identify the common factor of all the terms in the expression and use it to factor the expression.
Common factor = 3z
Hence, $3z^{3}-6z^{2}+9z$ = $3z(z^{2}-2z+3)$