Answer
$(x^3-4)(3x^3-2)$
Work Step by Step
The two numbers whose product is $ac=
3(8)=24
$ and whose sum is $b=
-14
$ are $\{
-12,-2
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3x^6-14x^3+8
$, is
\begin{array}{l}\require{cancel}
3x^6-12x^3-2x^3+8
\\\\=
(3x^6-12x^3)-(2x^3-8)
\\\\=
3x^3(x^3-4)-2(x^3-4)
\\\\=
(x^3-4)(3x^3-2)
.\end{array}
