Chapter 5 - Section 5.5 - The Greatest Common Factor and Factoring by Grouping - Exercise Set - Page 296: 102

$f(x)=2\left( 11x^2+137x+7814 \right)$

Factoring the $GCF=2,$ the given function, $ f(x)=22x^2+274x+15628 ,$ is equivalent to \begin{array}{l}\require{cancel} f(x)=2\left( \dfrac{22x^2}{2}+\dfrac{274x}{2}+\dfrac{15628}{2} \right) \\ f(x)=2\left( 11x^2+137x+7814 \right) .\end{array}