Answer
$(2g-1)(g-17)$
Work Step by Step
$2g^{2}-35g+17=$
...find factors of $ac$ with a sum of $b$.
($ac=34,\ b=-35$)
$\left[\begin{array}{lll}
\text{Factors of 34} & \text{Sum of factors} & \\
1\text{ and }34 & 35 & \\
-1\text{ and }-34 & -35 & \text{ is what we need }
\end{array}\right]$
...use the factors you found to rewrite $bx$.
$=2g^{2}-g-34g+17$
...factor by grouping.
$=g(2g-1)-17(2g-1)$
...use the Distributive Property.
$=(2g-1)(g-17)$
