Answer
$(z+2k)(z-8k)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
z^2-6zk-16k^2
,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$ in the quadratic expression $x^2+bx+c.$ Then, express the factored form as $(x+m_1)(x+m_2).$
$\bf{\text{Solution Details:}}$
In the expression above, the value of $c$ is $
-16
$ and the value of $b$ is $
-6
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,-16 \}, \{ 2,-8 \}, \{ 4,-8 \},
\\
\{ -1,16 \}, \{ -2,8 \}, \{ -4,8 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
2,-8
\}.$ Hence, the factored form of the expression above is
\begin{array}{l}\require{cancel}
(z+2k)(z-8k)
.\end{array}
