Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 45

$-4(x+5)^2$

Factoring the negative $GCF= -4 $, the given expression, $ -4x^2-40x-100 ,$ is equivalent to \begin{array}{l} -4(x^2+10x+25) .\end{array} The 2 numbers whose product is $ac= 1(25)=25 $ and whose sum is $b= 10 $ are $\left\{ 5,5 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} -4(x^2+5x+5x+25) \\\\= -4[(x^2+5x)+(5x+25)] \\\\= -4[x(x+5)+5(x+5)] \\\\= -4[(x+5)(x+5)] \\\\= -4(x+5)^2 .\end{array}