Find remainder when $ -9x^{2}+14x-8 $ is divided by $ 0 $.

The synthetic division table is:

$$ \begin{array}{c|rrr}0&-9&14&-8\\& & 0& \color{black}{0} \\ \hline &\color{blue}{-9}&\color{blue}{14}&\color{orangered}{-8} \end{array} $$

The remainder when $ -9x^{2}+14x-8 $ is divided by $ x $ is $ \, \color{red}{ -8 } $.

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.

$$ \begin{array}{c|rrr}\color{blue}{0}&-9&14&-8\\& & & \\ \hline &&& \end{array} $$

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

$$ \begin{array}{c|rrr}0&\color{orangered}{ -9 }&14&-8\\& & & \\ \hline &\color{orangered}{-9}&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -9 \right) } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrr}\color{blue}{0}&-9&14&-8\\& & \color{blue}{0} & \\ \hline &\color{blue}{-9}&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 14 } + \color{orangered}{ 0 } = \color{orangered}{ 14 } $

$$ \begin{array}{c|rrr}0&-9&\color{orangered}{ 14 }&-8\\& & \color{orangered}{0} & \\ \hline &-9&\color{orangered}{14}& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 14 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrr}\color{blue}{0}&-9&14&-8\\& & 0& \color{blue}{0} \\ \hline &-9&\color{blue}{14}& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ -8 } + \color{orangered}{ 0 } = \color{orangered}{ -8 } $

$$ \begin{array}{c|rrr}0&-9&14&\color{orangered}{ -8 }\\& & 0& \color{orangered}{0} \\ \hline &\color{blue}{-9}&\color{blue}{14}&\color{orangered}{-8} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -8 }\right) $.

Synthetic Division Calculator