Divide using synthetic division $$ ( 8x^{4}-24x^{3}+3x^{2}-15x+11 ) \div ( 0 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrrrr}0&8&-24&3&-15&11\\& & 0& 0& 0& \color{black}{0} \\ \hline &\color{blue}{8}&\color{blue}{-24}&\color{blue}{3}&\color{blue}{-15}&\color{orangered}{11} \end{array} $$The solution is:
$$ \dfrac{ 8x^{4}-24x^{3}+3x^{2}-15x+11 }{ x } = \color{blue}{8x^{3}-24x^{2}+3x-15} ~+~ \dfrac{ \color{red}{ 11 } }{ x } $$Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.
$$ \begin{array}{c|rrrrr}\color{blue}{0}&8&-24&3&-15&11\\& & & & & \\ \hline &&&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrrr}0&\color{orangered}{ 8 }&-24&3&-15&11\\& & & & & \\ \hline &\color{orangered}{8}&&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 8 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{0}&8&-24&3&-15&11\\& & \color{blue}{0} & & & \\ \hline &\color{blue}{8}&&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -24 } + \color{orangered}{ 0 } = \color{orangered}{ -24 } $
$$ \begin{array}{c|rrrrr}0&8&\color{orangered}{ -24 }&3&-15&11\\& & \color{orangered}{0} & & & \\ \hline &8&\color{orangered}{-24}&&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -24 \right) } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{0}&8&-24&3&-15&11\\& & 0& \color{blue}{0} & & \\ \hline &8&\color{blue}{-24}&&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 3 } + \color{orangered}{ 0 } = \color{orangered}{ 3 } $
$$ \begin{array}{c|rrrrr}0&8&-24&\color{orangered}{ 3 }&-15&11\\& & 0& \color{orangered}{0} & & \\ \hline &8&-24&\color{orangered}{3}&& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 3 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{0}&8&-24&3&-15&11\\& & 0& 0& \color{blue}{0} & \\ \hline &8&-24&\color{blue}{3}&& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ -15 } + \color{orangered}{ 0 } = \color{orangered}{ -15 } $
$$ \begin{array}{c|rrrrr}0&8&-24&3&\color{orangered}{ -15 }&11\\& & 0& 0& \color{orangered}{0} & \\ \hline &8&-24&3&\color{orangered}{-15}& \end{array} $$Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -15 \right) } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{0}&8&-24&3&-15&11\\& & 0& 0& 0& \color{blue}{0} \\ \hline &8&-24&3&\color{blue}{-15}& \end{array} $$Step 9 : Add down last column: $ \color{orangered}{ 11 } + \color{orangered}{ 0 } = \color{orangered}{ 11 } $
$$ \begin{array}{c|rrrrr}0&8&-24&3&-15&\color{orangered}{ 11 }\\& & 0& 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{8}&\color{blue}{-24}&\color{blue}{3}&\color{blue}{-15}&\color{orangered}{11} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 8x^{3}-24x^{2}+3x-15 } $ with a remainder of $ \color{red}{ 11 } $.