Answer
$\left( 2a+5b \right)\left( 3a-2b \right)$
Work Step by Step
$6{{a}^{2}}+11ab-10{{b}^{2}}$
Arranging the function in pairs,
$6{{a}^{2}}+15ab-4ab-10{{b}^{2}}$
$3a\left( 2a+5b \right)-2b\left( 2a+5b \right)$
Factoring out $\left( 2a+5b \right)$:
$\left( 2a+5b \right)\left( 3a-2b \right)$
Thus, the factor of the function, $6{{a}^{2}}+11ab-10{{b}^{2}}$, is $\left( 2a+5b \right)\left( 3a-2b \right)$.
Check,
$\begin{align}
& \left( 2a+5b \right)\left( 3a-2b \right)=2a\cdot 3a-2a\cdot 2b+5b\cdot 3a-5b\cdot 2b \\
& =6{{a}^{2}}-4ab+15ab-10{{b}^{2}} \\
& =6{{a}^{2}}+11ab-10{{b}^{2}}
\end{align}$
The answer checks.
