Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 58

$(3x-7)(8x+3)$

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}