Answer
$3x^2(2x+1)(3x+2)$
Work Step by Step
Factoring the $GCF=3x^2$, then the given expression, $
18x^4+21x^3+6x^2
$, is equivalent to $
3x^2(6x^2+7x+2)
$.\\
The two numbers whose product is $ac=
6(2)=12
$ and whose sum is $b=
7
$ are $\{
3,4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3x^2(6x^2+7x+2)
$, is
\begin{array}{l}\require{cancel}
3x^2(6x^2+3x+4x+2)
\\\\=
3x^2[(6x^2+3x)+(4x+2)]
\\\\=
3x^2[3x(2x+1)+2(2x+1)]
\\\\=
3x^2[(2x+1)(3x+2)]
\\\\=
3x^2(2x+1)(3x+2)
.\end{array}
