Find remainder when $ 7x^{3}+10x-16 $ is divided by $ 2 $.

The synthetic division table is:

$$ \begin{array}{c|rrrr}0&7&0&10&-16\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{7}&\color{blue}{0}&\color{blue}{10}&\color{orangered}{-16} \end{array} $$

The remainder when $ 7x^{3}+10x-16 $ is divided by $ x $ is $ \, \color{red}{ -16 } $.

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.

$$ \begin{array}{c|rrrr}\color{blue}{0}&7&0&10&-16\\& & & & \\ \hline &&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}0&\color{orangered}{ 7 }&0&10&-16\\& & & & \\ \hline &\color{orangered}{7}&&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 7 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&7&0&10&-16\\& & \color{blue}{0} & & \\ \hline &\color{blue}{7}&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}0&7&\color{orangered}{ 0 }&10&-16\\& & \color{orangered}{0} & & \\ \hline &7&\color{orangered}{0}&& \end{array} $$

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 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&7&0&10&-16\\& & 0& \color{blue}{0} & \\ \hline &7&\color{blue}{0}&& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ 10 } + \color{orangered}{ 0 } = \color{orangered}{ 10 } $

$$ \begin{array}{c|rrrr}0&7&0&\color{orangered}{ 10 }&-16\\& & 0& \color{orangered}{0} & \\ \hline &7&0&\color{orangered}{10}& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 10 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&7&0&10&-16\\& & 0& 0& \color{blue}{0} \\ \hline &7&0&\color{blue}{10}& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ -16 } + \color{orangered}{ 0 } = \color{orangered}{ -16 } $

$$ \begin{array}{c|rrrr}0&7&0&10&\color{orangered}{ -16 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{7}&\color{blue}{0}&\color{blue}{10}&\color{orangered}{-16} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -16 }\right) $.

Synthetic Division Calculator