Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set - Page 303: 43

$(x-27)(x+3)$

The two numbers whose product is $ac= 1(-81)=-81 $ and whose sum is $b= -24 $ are $\{ -27,3 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ x^2-24x-81 $, is \begin{array}{l}\require{cancel} x^2-27x+3x-81 \\\\= (x^2-27x)+(3x-81) \\\\= x(x-27)+3(x-27) \\\\= (x-27)(x+3) .\end{array}