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