Answer
$(m^2-5)(m^2+2)$
Work Step by Step
Let $z=m^2.$ Then the given expression, $
m^4-3m^2-10
,$ is equivalent to
\begin{array}{l}\require{cancel}
z^2-3z-10
.\end{array}
The two numbers whose product is $ac=
1(-10)=-10
$ and whose sum is $b=
-3
$ are $\{
-5,2
\}.$ Using these two numbers to decompose the middle term, then the factored form of $
z^2-3z-10
$ is
\begin{array}{l}\require{cancel}
z^2-5z+2z-10
\\\\=
(z^2-5z)+(2z-10)
\\\\=
z(z-5)+2(z-5)
\\\\=
(z-5)(z+2)
.\end{array}
Since $z=m^2$, then the expression $
(z-5)(z+2)
$ is equivalent to
\begin{array}{l}\require{cancel}
(m^2-5)(m^2+2)
.\end{array}
