Answer
$\text{B}$
Work Step by Step
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(m-5)(m+4)+8
,$ is equivalent to
\begin{align*}
&
m(m)+m(4)-5(m)-5(4)+8
\\&=
m^2+4m-5m-20+8
\\&=
m^2+(4m-5m)+(-20+8)
\\&=
m^2+(-m)+(-12)
\\&=
m^2-m-12
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c=
-12
$ and $b=
-1
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,3
\right\}.$ Using these two numbers, the factored form of the $\text{
expression
}$ above is
\begin{align*}
(m-4)(m+3)
.\end{align*}
Hence, Choice B.
