Answer
$-2x^2 \left( x^{3}-3x-2 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
First, get the $GCF$ of the given expression, $
-2x^5+6x^3+4x^2
.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. Finally, factor out the $-1$.
$\bf{\text{Solution Details:}}$
The $GCF$ of the constants of the terms $\{
-2,6,4
\}$ is $
2
.$ The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{
x^5,x^3,x^2
\}$ is $
x^2
.$ Hence, the entire expression has $GCF=
2x^2
.$
Factoring the $GCF=
2x^2
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
2x^2 \left( \dfrac{-2x^5}{2x^2}+\dfrac{6x^3}{2x^2}+\dfrac{4x^2}{2x^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}
2x^2 \left( -x^{5-2}+3x^{3-2}+2x^{2-2} \right)
\\\\=
2x^2 \left( -x^{3}+3x^{1}+2x^{0} \right)
\\\\=
2x^2 \left( -x^{3}+3x+2(1) \right)
\\\\=
2x^2 \left( -x^{3}+3x+2 \right)
.\end{array}
Factoring out $-1$ from the second factor results to
\begin{array}{l}\require{cancel}
-2x^2 \left( x^{3}-3x-2 \right)
.\end{array}