Divide using synthetic division $$ ( x^{5}-4x^{4}-49x^{3}+27x^{2}+87x-48 ) \div ( x-9 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrrrrr}9&1&-4&-49&27&87&-48\\& & 9& 45& -36& -81& \color{black}{54} \\ \hline &\color{blue}{1}&\color{blue}{5}&\color{blue}{-4}&\color{blue}{-9}&\color{blue}{6}&\color{orangered}{6} \end{array} $$The solution is:
$$ \dfrac{ x^{5}-4x^{4}-49x^{3}+27x^{2}+87x-48 }{ x-9 } = \color{blue}{x^{4}+5x^{3}-4x^{2}-9x+6} ~+~ \dfrac{ \color{red}{ 6 } }{ x-9 } $$Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -9 = 0 $ ( $ x = \color{blue}{ 9 } $ ) at the left.
$$ \begin{array}{c|rrrrrr}\color{blue}{9}&1&-4&-49&27&87&-48\\& & & & & & \\ \hline &&&&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrrrr}9&\color{orangered}{ 1 }&-4&-49&27&87&-48\\& & & & & & \\ \hline &\color{orangered}{1}&&&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 9 } \cdot \color{blue}{ 1 } = \color{blue}{ 9 } $.
$$ \begin{array}{c|rrrrrr}\color{blue}{9}&1&-4&-49&27&87&-48\\& & \color{blue}{9} & & & & \\ \hline &\color{blue}{1}&&&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -4 } + \color{orangered}{ 9 } = \color{orangered}{ 5 } $
$$ \begin{array}{c|rrrrrr}9&1&\color{orangered}{ -4 }&-49&27&87&-48\\& & \color{orangered}{9} & & & & \\ \hline &1&\color{orangered}{5}&&&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 9 } \cdot \color{blue}{ 5 } = \color{blue}{ 45 } $.
$$ \begin{array}{c|rrrrrr}\color{blue}{9}&1&-4&-49&27&87&-48\\& & 9& \color{blue}{45} & & & \\ \hline &1&\color{blue}{5}&&&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -49 } + \color{orangered}{ 45 } = \color{orangered}{ -4 } $
$$ \begin{array}{c|rrrrrr}9&1&-4&\color{orangered}{ -49 }&27&87&-48\\& & 9& \color{orangered}{45} & & & \\ \hline &1&5&\color{orangered}{-4}&&& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 9 } \cdot \color{blue}{ \left( -4 \right) } = \color{blue}{ -36 } $.
$$ \begin{array}{c|rrrrrr}\color{blue}{9}&1&-4&-49&27&87&-48\\& & 9& 45& \color{blue}{-36} & & \\ \hline &1&5&\color{blue}{-4}&&& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ 27 } + \color{orangered}{ \left( -36 \right) } = \color{orangered}{ -9 } $
$$ \begin{array}{c|rrrrrr}9&1&-4&-49&\color{orangered}{ 27 }&87&-48\\& & 9& 45& \color{orangered}{-36} & & \\ \hline &1&5&-4&\color{orangered}{-9}&& \end{array} $$Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 9 } \cdot \color{blue}{ \left( -9 \right) } = \color{blue}{ -81 } $.
$$ \begin{array}{c|rrrrrr}\color{blue}{9}&1&-4&-49&27&87&-48\\& & 9& 45& -36& \color{blue}{-81} & \\ \hline &1&5&-4&\color{blue}{-9}&& \end{array} $$Step 9 : Add down last column: $ \color{orangered}{ 87 } + \color{orangered}{ \left( -81 \right) } = \color{orangered}{ 6 } $
$$ \begin{array}{c|rrrrrr}9&1&-4&-49&27&\color{orangered}{ 87 }&-48\\& & 9& 45& -36& \color{orangered}{-81} & \\ \hline &1&5&-4&-9&\color{orangered}{6}& \end{array} $$Step 10 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 9 } \cdot \color{blue}{ 6 } = \color{blue}{ 54 } $.
$$ \begin{array}{c|rrrrrr}\color{blue}{9}&1&-4&-49&27&87&-48\\& & 9& 45& -36& -81& \color{blue}{54} \\ \hline &1&5&-4&-9&\color{blue}{6}& \end{array} $$Step 11 : Add down last column: $ \color{orangered}{ -48 } + \color{orangered}{ 54 } = \color{orangered}{ 6 } $
$$ \begin{array}{c|rrrrrr}9&1&-4&-49&27&87&\color{orangered}{ -48 }\\& & 9& 45& -36& -81& \color{orangered}{54} \\ \hline &\color{blue}{1}&\color{blue}{5}&\color{blue}{-4}&\color{blue}{-9}&\color{blue}{6}&\color{orangered}{6} \end{array} $$Bottom line represents the quotient $ \color{blue}{ x^{4}+5x^{3}-4x^{2}-9x+6 } $ with a remainder of $ \color{red}{ 6 } $.