Answer
$(x^2+3)(x^2-2)$
Work Step by Step
Let $z=x^2$. Then the given expression, $
x^4+x^2-6
$, is equivalent to $
z^2+z-6
$.
The two numbers whose product is $ac=
1(-6)=-6
$ and whose sum is $b=
1
$ are $\{
3,-2
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
z^2+z-6
$, is
\begin{array}{l}\require{cancel}
z^2+3z-2z-6
\\\\=
(z^2+3z)-(2z+6)
\\\\=
z(z+3)-2(z+3)
\\\\=
(z+3)(z-2)
.\end{array}
Since $z=x^2$, then the factored form of the original expression is $
(x^2+3)(x^2-2)
$.
