Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 34

$-c^2(c+8)(c-7)$

Factoring the negative $GCF= -c^2 $, the given expression, $ -c^4-c^3+56c^2 ,$ is equivalent to \begin{array}{l} -c^2(c^2+c-56) .\end{array} The 2 numbers whose product is $ac= 1(-56)=-56 $ and whose sum is $b= 1 $ are $\left\{ 8,-7 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} -c^2(c^2+8c-7c-56) \\\\= -c^2[(c^2+8c)-(7c+56)] \\\\= -c^2[c(c+8)-7(c+8)] \\\\= -c^2[(c+8)(c-7)] \\\\= -c^2(c+8)(c-7) .\end{array}