Answer
$2(x+1)(3x+1)$
Work Step by Step
Factor out $2$.
$6x^2+8x+2=2(3x^2+4x+1)$
Rewrite $4x$ as $3x+1x$.
$=2(3x^2+3x+1x+1)$
Group the first two terms together and group the last two terms together.
$=2[(3x^2+3x)+(1x+1)]$
Factor out the GCF in each group.
$=2[3x(x+1)+1(x+1)]$
Factor out $(x+1)$.
$=2(x+1)(3x+1)$
Hence, the completely factored form of the given expression is $2(x+1)(3x+1)$.
