Intermediate Algebra (12th Edition)

$(k-8)(k+2)$
$\bf{\text{Solution Outline:}}$ 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}