Answer
The factor of the polynomial $5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x$ is$x\left( x-2 \right)\left( 5{{x}^{2}}-3 \right)$.
Work Step by Step
$5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x$
The factor of the polynomial $5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x$ is calculated as follows.
$5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x=\left( 5{{x}^{3}}\cdot x-10{{x}^{2}}\cdot x-3x\cdot x+6\cdot x \right)$
Use the distributive property;
$5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x=x\left( 5{{x}^{3}}-10{{x}^{2}}-3x+6 \right)$
Group the terms as follows:
$\begin{align}
& 5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x=x\left( 5{{x}^{3}}-10{{x}^{2}}-3x+6 \right) \\
& =x\left[ 5{{x}^{2}}\left( x-2 \right)-3\left( x-2 \right) \right]
\end{align}$
Factor out the common binomial factor$\left( x-2 \right)$.
$\begin{align}
& 5{{x}^{4}}-10{{x}^{3}}-3{{x}^{2}}+6x=x\left[ 5{{x}^{2}}\left( x-2 \right)-3\left( x-2 \right) \right] \\
& =x\left( x-2 \right)\left( 5{{x}^{2}}-3 \right)
\end{align}$
