Answer
$(z-5p)(z+4p)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
z^2-zp-20p^2
,$ use the factoring of trinomials in the form $x^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $b=
-1
,\text{ and } c=
-20
.$ Using the factoring of trinomials in the form $x^2+bx+c,$ the two numbers whose product is $c$ and whose sum is $b$ are $\left\{
-5,4
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{array}{l}\require{cancel}
(z-5p)(z+4p)
.\end{array}