Answer
a. $\quad3x^{2}(3x^{4}+5x^{2}+4)$
b. $\quad-6x^{2}(x^{2}+3x+2)$
Work Step by Step
a.
$ 9x^{6}+15x^{4}+12x^{2}\qquad$
...to factor the polynomial, first factor each term.
$9x^{6}=(3)\cdot 3\cdot[x\cdot x]\cdot x\cdot x\cdot x\cdot x$
$15x^{4}=(3)\cdot 5\cdot[x\cdot x]\cdot x\cdot x$
$12x^{2}=2\cdot 2\cdot(3)\cdot[x\cdot x]$
GCF= $(3)\cdot[x\cdot x]$, or $3x^{2}$.
$ 9x^{6}+15x^{4}+12x^{2}\qquad$
...factor out the GCF from each term
$=3x^{2}(3x^{4})+3x^{2}(5x^{2})+3x^{2}(4)\qquad$
...apply the Distributive Property.
$=3x^{2}(3x^{4}+5x^{2}+4)$
b.
$-6x^{4}=(-1)\cdot(2)\cdot(3)\cdot(x\cdot x)\cdot x\cdot x$
$-18x^{3}=(-1)\cdot(2)\cdot(3)\cdot 3\cdot(x\cdot x)\cdot x$
$-12x^{2}=(-1)\cdot(2)\cdot 2\cdot(3)\cdot(x\cdot x)$
GCF=$(-1)\cdot(2)\cdot(3)\cdot(x\cdot x)$, or $-6x^{2}$.
$-6x^{2}(x^{2}+3x+2)$
