Answer
$7(3z-7)(z-1)$
Work Step by Step
$21z^{2}-70z+49=$
...factor out the GCF.
$=7(3z^{2}-10z+7)$
...find factors of $ac$ with a sum of $b$.
($ac=21,\ b=-10$)
$\left[\begin{array}{lll}
\text{Factors of 21} & \text{Sum of factors} & \\
1\text{ and }21 & 22 & \\
-1\text{ and }-21 & -22 & \\
3\text{ and }7 & 10 & \\
-3\text{ and }-7 & -10 & \text{ is what we need }
\end{array}\right]$
...use the factors you found to rewrite $bx$.
$=7(3z^{2}-3z-7z+7)$
...factor by grouping.
$=7[3z(z-1)-7(z-1)]$
...factor again.
$=7(3z-7)(z-1)$
