Answer
GCF=$4g$
$4g(g+2)$
Work Step by Step
Find the GCF of the term of each polynomial. Then factor the polynomial.
$4g^{2}+8g$
Both terms have a $g$ in them so the GCF must have a $g$
Both of the coefficients are divisible by $4$ so the GCF must have a $4$
GCF=$4g$
Factor:
$4g(g+2)$