Answer
$(z^2-3)(4z^2+5)$
Work Step by Step
The two numbers whose product is $ac=
4(-15)=-60
$ and whose sum is $b=
-7
$ are $\{
-12,5
\}$. Using these two numbers to decompose the middle term of the expression, $
4z^4-7z^2-15
,$ then the factored form is
\begin{array}{l}\require{cancel}
4z^4-12z^2+5z^2-15
\\\\=
(4z^4-12z^2)+(5z^2-15)
\\\\=
4z^2(z^2-3)+5(z^2-3)
\\\\=
(z^2-3)(4z^2+5)
.\end{array}
