Answer
$6x^{2}yz(4xy^{2}z^{2}+5y+3z)$
Work Step by Step
1. Determine the greatest common factor of all terms in the polynomial.
$24=6\times 4,\quad 30=6\times 5,\quad 18=6\times 3,$
the greatest integer factor is $6.$
The variable part of the greatest common factor always contains the smallest power of a variable that appears in all terms of the polynomial.
Here, it is $x^{2}yz .$
$GCF=6x^{2}yz .$
2. Express each term as the product of the GCF and its other factor.
$ \begin{array}{lll}
24x^{3}y^{3}z^{3} & +30x^{2}y^{2}z & +18x^{2}yz^{2}=\\
=6x^{2}yz\cdot 4xy^{2}z^{2} & +6x^{2}yz\cdot 5y & +6x^{2}yz\cdot 3z
\end{array}$
3. Use the distributive property to factor out the GCF.
= $6x^{2}yz(4xy^{2}z^{2}+5y+3z)$