Answer
$-11x(x-4)(x-6)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
First, factor the GCF of the terms. Then, to factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Express the factored form as $GCF(x+m_1)(x+m_2).$
$\bf{\text{Solution Details:}}$
Using the negative $GCF=
-11x
,$ the given expression, $
-11x^3+110x^2-264x
,$ is equivalent to
\begin{array}{l}\require{cancel}
-11x(x^2-10x+24)
.\end{array}
In the expression above, the value of $c$ is $
24
$ and the value of $b$ is $
-10
.$
The possible pairs of integers whose product is $ac$ are
\begin{array}{l}\require{cancel}
\{1,24\}, \{2,12\}, \{3,8\}, \{4,6\},
\{-1,-24\}, \{-2,-12\}, \{-3,-8\}, \{-4,-6\}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
-4,-6
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
-11x(x-4)(x-6)
.\end{array}
