Find remainder when $ x^{3}+5x^{2}-26x-32 $ is divided by $ 2 $.

The synthetic division table is:

$$ \begin{array}{c|rrrr}0&1&5&-26&-32\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{1}&\color{blue}{5}&\color{blue}{-26}&\color{orangered}{-32} \end{array} $$

The remainder when $ x^{3}+5x^{2}-26x-32 $ is divided by $ x $ is $ \, \color{red}{ -32 } $.

We can find remainder using synthetic division method.

Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.

$$ \begin{array}{c|rrrr}\color{blue}{0}&1&5&-26&-32\\& & & & \\ \hline &&&& \end{array} $$

Step 1 : Bring down the leading coefficient to the bottom row.

$$ \begin{array}{c|rrrr}0&\color{orangered}{ 1 }&5&-26&-32\\& & & & \\ \hline &\color{orangered}{1}&&& \end{array} $$

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 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&1&5&-26&-32\\& & \color{blue}{0} & & \\ \hline &\color{blue}{1}&&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 5 } + \color{orangered}{ 0 } = \color{orangered}{ 5 } $

$$ \begin{array}{c|rrrr}0&1&\color{orangered}{ 5 }&-26&-32\\& & \color{orangered}{0} & & \\ \hline &1&\color{orangered}{5}&& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 5 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&1&5&-26&-32\\& & 0& \color{blue}{0} & \\ \hline &1&\color{blue}{5}&& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ -26 } + \color{orangered}{ 0 } = \color{orangered}{ -26 } $

$$ \begin{array}{c|rrrr}0&1&5&\color{orangered}{ -26 }&-32\\& & 0& \color{orangered}{0} & \\ \hline &1&5&\color{orangered}{-26}& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -26 \right) } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&1&5&-26&-32\\& & 0& 0& \color{blue}{0} \\ \hline &1&5&\color{blue}{-26}& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ -32 } + \color{orangered}{ 0 } = \color{orangered}{ -32 } $

$$ \begin{array}{c|rrrr}0&1&5&-26&\color{orangered}{ -32 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{1}&\color{blue}{5}&\color{blue}{-26}&\color{orangered}{-32} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -32 }\right) $.

Synthetic Division Calculator