Answer
$8x^{2}yz (2yz+4z+3)$
Work Step by Step
1. Determine the greatest common factor of all terms in the polynomial.
$16=8\times 2,\quad 32=8\times 4,\quad 24=8\times 3,$
the greatest integer factor is $8.$
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 $x^{2}yz .$
$GCF=8x^{2}yz .$
2. Express each term as the product of the GCF and its other factor.
$ \begin{array}{lll}
16x^{2}y^{2}z^{2} & +32x^{2}yz^{2} & +24x^{2}yz=\\
=8x^{2}yz \cdot 2yz & +8x^{2}yz \cdot 4z & +8x^{2}yz \cdot 3
\end{array}$
3. Use the distributive property to factor out the GCF.
= $8x^{2}yz (2yz+4z+3)$
