Answer
$6x(2x^{3}+5x^{2}+7)$
Work Step by Step
List the factors of each term, note the common factors:
$12x^{4}=2\cdot(2\cdot 3)\cdot(x)\cdot x\cdot x\cdot x$
$30x^{3}=(2\cdot 3)\cdot 5\cdot(x)\cdot x\cdot x$
$42x=(2\cdot 3)\cdot 7\cdot(x)$
GCF=$(2\cdot 3)\cdot(x)$, or $6x$.
$12x^{4}+30x^{3}+42x$= ...factor out the GCF from each term.
$=6x(2x^{3})+6x(5x^{2})+6x(7)$
...apply the Distributive Property.
=$6x(2x^{3}+5x^{2}+7)$
