Divide using synthetic division $$ ( x^{3}+17x^{2}+70x-54 ) \div ( -1 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrrr}0&1&17&70&-54\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{1}&\color{blue}{17}&\color{blue}{70}&\color{orangered}{-54} \end{array} $$The solution is:
$$ \dfrac{ x^{3}+17x^{2}+70x-54 }{ x } = \color{blue}{x^{2}+17x+70} \color{red}{~-~} \dfrac{ \color{red}{ 54 } }{ x } $$Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.
$$ \begin{array}{c|rrrr}\color{blue}{0}&1&17&70&-54\\& & & & \\ \hline &&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrr}0&\color{orangered}{ 1 }&17&70&-54\\& & & & \\ \hline &\color{orangered}{1}&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 1 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&1&17&70&-54\\& & \color{blue}{0} & & \\ \hline &\color{blue}{1}&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 17 } + \color{orangered}{ 0 } = \color{orangered}{ 17 } $
$$ \begin{array}{c|rrrr}0&1&\color{orangered}{ 17 }&70&-54\\& & \color{orangered}{0} & & \\ \hline &1&\color{orangered}{17}&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 17 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&1&17&70&-54\\& & 0& \color{blue}{0} & \\ \hline &1&\color{blue}{17}&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 70 } + \color{orangered}{ 0 } = \color{orangered}{ 70 } $
$$ \begin{array}{c|rrrr}0&1&17&\color{orangered}{ 70 }&-54\\& & 0& \color{orangered}{0} & \\ \hline &1&17&\color{orangered}{70}& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 70 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&1&17&70&-54\\& & 0& 0& \color{blue}{0} \\ \hline &1&17&\color{blue}{70}& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ -54 } + \color{orangered}{ 0 } = \color{orangered}{ -54 } $
$$ \begin{array}{c|rrrr}0&1&17&70&\color{orangered}{ -54 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{1}&\color{blue}{17}&\color{blue}{70}&\color{orangered}{-54} \end{array} $$Bottom line represents the quotient $ \color{blue}{ x^{2}+17x+70 } $ with a remainder of $ \color{red}{ -54 } $.