Answer
$(x^2-5)(x^2+4)$
Work Step by Step
Let $z=x^2$. Then the given expression, $
x^4-x^2-20
$, is equivalent to $
z^2-z-20
$.
The two numbers whose product is $ac=
1(-20)=-20
$ and whose sum is $b=
-1
$ are $\{
4,-5
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
z^2-z-20
$, is
\begin{array}{l}\require{cancel}
z^2-5z+4z-20
\\\\=
(z^2-5z)+(4z-20)
\\\\=
z(z-5)+4(z-5)
\\\\=
(z-5)(z+4)
.\end{array}
Since $z=x^2$, then the factored form of the original expression is $
(x^2-5)(x^2+4)
$.
