Divide using synthetic division $$ ( -8x^{6} ) \div ( 0 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrrrrrr}0&-8&0&0&0&0&0&0\\& & 0& 0& 0& 0& 0& \color{black}{0} \\ \hline &\color{blue}{-8}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{orangered}{0} \end{array} $$The solution is:
$$ \dfrac{ -8x^{6} }{ x } = \color{blue}{-8x^{5}} $$Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & & & & & & \\ \hline &&&&&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrrrrr}0&\color{orangered}{ -8 }&0&0&0&0&0&0\\& & & & & & & \\ \hline &\color{orangered}{-8}&&&&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -8 \right) } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & \color{blue}{0} & & & & & \\ \hline &\color{blue}{-8}&&&&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 0 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrrrr}0&-8&\color{orangered}{ 0 }&0&0&0&0&0\\& & \color{orangered}{0} & & & & & \\ \hline &-8&\color{orangered}{0}&&&&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 0 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & 0& \color{blue}{0} & & & & \\ \hline &-8&\color{blue}{0}&&&&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 0 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrrrr}0&-8&0&\color{orangered}{ 0 }&0&0&0&0\\& & 0& \color{orangered}{0} & & & & \\ \hline &-8&0&\color{orangered}{0}&&&& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 0 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & 0& 0& \color{blue}{0} & & & \\ \hline &-8&0&\color{blue}{0}&&&& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 0 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrrrr}0&-8&0&0&\color{orangered}{ 0 }&0&0&0\\& & 0& 0& \color{orangered}{0} & & & \\ \hline &-8&0&0&\color{orangered}{0}&&& \end{array} $$Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 0 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & 0& 0& 0& \color{blue}{0} & & \\ \hline &-8&0&0&\color{blue}{0}&&& \end{array} $$Step 9 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 0 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrrrr}0&-8&0&0&0&\color{orangered}{ 0 }&0&0\\& & 0& 0& 0& \color{orangered}{0} & & \\ \hline &-8&0&0&0&\color{orangered}{0}&& \end{array} $$Step 10 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 0 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & 0& 0& 0& 0& \color{blue}{0} & \\ \hline &-8&0&0&0&\color{blue}{0}&& \end{array} $$Step 11 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 0 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrrrr}0&-8&0&0&0&0&\color{orangered}{ 0 }&0\\& & 0& 0& 0& 0& \color{orangered}{0} & \\ \hline &-8&0&0&0&0&\color{orangered}{0}& \end{array} $$Step 12 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 0 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrrrr}\color{blue}{0}&-8&0&0&0&0&0&0\\& & 0& 0& 0& 0& 0& \color{blue}{0} \\ \hline &-8&0&0&0&0&\color{blue}{0}& \end{array} $$Step 13 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 0 } = \color{orangered}{ 0 } $
$$ \begin{array}{c|rrrrrrr}0&-8&0&0&0&0&0&\color{orangered}{ 0 }\\& & 0& 0& 0& 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{-8}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{orangered}{0} \end{array} $$Bottom line represents the quotient $ \color{blue}{ -8x^{5} } $ with a remainder of $ \color{red}{ 0 } $.