Answer
$(x^3+3)(2x^3-3)$
Work Step by Step
The two numbers whose product is $ac=
2(-9)=-18
$ and whose sum is $b=
3
$ are $\{
6,-3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2x^6+3x^3-9
$, is
\begin{array}{l}\require{cancel}
2x^6+6x^3-3x^3-9
\\\\=
(2x^6+6x^3)-(3x^3+9)
\\\\=
2x^3(x^3+3)-3(x^3+3)
\\\\=
(x^3+3)(2x^3-3)
.\end{array}
