Answer
$(3x-7)(8x+3)$
Work Step by Step
The two numbers whose product is $ac=
24(-21)=-504
$ and whose sum is $b=
-47
$ are $\{
-56,9
\}$. Using these two numbers to decompose the middle term of the expression, $
24x^2-47x-21
,$ then the factored form is
\begin{array}{l}
24x^2-56x+9x-21
\\\\=
(24x^2-56x)+(9x-21)
\\\\=
8x(3x-7)+3(3x-7)
\\\\=
(3x-7)(8x+3)
.\end{array}