Answer
$(5-x)^2 \left( 7-2x \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
2(5-x)^3-3(5-x)^2
.$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
2,-3
\}$ is $
1
.$ The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variables $\{
(5-x)^3,(5-x)^2
\}$ is $
(5-x)^2
.$ Hence, the entire expression has $GCF=
(5-x)^2
.$
Factoring the $GCF=
(5-x)^2
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(5-x)^2 \left( \dfrac{2(5-x)^3}{(5-x)^2}-\dfrac{3(5-x)^2}{(5-x)^2} \right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
(5-x)^2 \left( 2(5-x)^{3-2}-3(5-x)^{2-2} \right)
\\\\=
(5-x)^2 \left( 2(5-x)^{1}-3(5-x)^{0} \right)
\\\\=
(5-x)^2 \left( 2(5-x)-3(1) \right)
\\\\=
(5-x)^2 \left( 10-2x-3 \right)
\\\\=
(5-x)^2 \left( 7-2x \right)
.\end{array}
