Answer
$(r-5)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
r^2-r-20
,$ 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 given expression, the value of $c$ is $
-20
$ and the value of $b$ is $
-1
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,-20 \}, \{ 2,-10 \}, \{ 4,-5 \},
\{ -1,20 \}, \{ -2,10 \}, \{ -4,5 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
4,-5
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
(r+4)(r-5)
.\end{array}
The missing factor in the given expression is $
(r-5)
.$