#### Answer

$4x(x^2+2x+3)$

#### Work Step by Step

Find the greatest common factor. Find the factors of each term and multiply the factors that are common to all the terms.
$4x^3=\underline2\times\underline2\times\underline x\times x\times x$
$8x^2=\underline2\times\underline2\times2\times\underline x\times x$
$12x=3\times\underline2\times\underline2\times\underline x$
GCF=$2\times2\times x=4x$
Factor the GCF out of each term. Use the factors from each term that are not part of the GCF.
$4x^3+8x^2+12x=4x(x^2+2x+3)$