Answer
$6(x^{2}+x+1)$
Work Step by Step
$6x^{2}+6x+6$
The prime factorization of $6x^{2}$ is $[2\cdot 3]\cdot x\cdot x$
The prime factorization of $6x$ is $[2\cdot 3]\cdot x$
The prime factorization of $6$ is$ [2\cdot 3]$
The largest common factor is $2\cdot 3=6$
Factor out $6$ from the given expression.
$=6(x^{2}+x+1)$
