Answer
$(2x+7)(5x-2)$
Work Step by Step
Find factors of $ac$ that have a sum of $b$.
Since $ac=-140$ and $b=31$,
find factors of $-140$ with a sum of $31$.
$\left[ \begin{array}{lcl}
\text{Factors of -140 } & \text{Sum of factors} & \\
1\text{ and }-140 & -139 & \\
-1\text{ and }140 & 139 & \\
2\text{ and }-70 & -68 & \\
-2\text{ and }70 & 68 & \\
4\text{ and }-35 & -31 & \\
-4\text{ and }35 & 31 & \text{...is what we need}
\end{array}\right]$
$10x^{2}+31x-14$
......use the factors to rewrite $bx$.
$=10x^{2}-4x+35x-14$
...factor out the GCF out of each pair of terms.
$=2x(5x-2)+7(5x-2)$
...use the Distributive Property.
$=(2x+7)(5x-2)$
