Find remainder when $ -2x^{3}-5x^{2}-3x+9 $ is divided by $ -3 $.

The synthetic division table is:

$$ \begin{array}{c|rrrr}0&-2&-5&-3&9\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{-2}&\color{blue}{-5}&\color{blue}{-3}&\color{orangered}{9} \end{array} $$

The remainder when $ -2x^{3}-5x^{2}-3x+9 $ is divided by $ x $ is $ \, \color{red}{ 9 } $.

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.

$$ \begin{array}{c|rrrr}\color{blue}{0}&-2&-5&-3&9\\& & & & \\ \hline &&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}0&\color{orangered}{ -2 }&-5&-3&9\\& & & & \\ \hline &\color{orangered}{-2}&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}\color{blue}{0}&-2&-5&-3&9\\& & \color{blue}{0} & & \\ \hline &\color{blue}{-2}&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}0&-2&\color{orangered}{ -5 }&-3&9\\& & \color{orangered}{0} & & \\ \hline &-2&\color{orangered}{-5}&& \end{array} $$

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

$$ \begin{array}{c|rrrr}\color{blue}{0}&-2&-5&-3&9\\& & 0& \color{blue}{0} & \\ \hline &-2&\color{blue}{-5}&& \end{array} $$

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

$$ \begin{array}{c|rrrr}0&-2&-5&\color{orangered}{ -3 }&9\\& & 0& \color{orangered}{0} & \\ \hline &-2&-5&\color{orangered}{-3}& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -3 \right) } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&-2&-5&-3&9\\& & 0& 0& \color{blue}{0} \\ \hline &-2&-5&\color{blue}{-3}& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ 9 } + \color{orangered}{ 0 } = \color{orangered}{ 9 } $

$$ \begin{array}{c|rrrr}0&-2&-5&-3&\color{orangered}{ 9 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{-2}&\color{blue}{-5}&\color{blue}{-3}&\color{orangered}{9} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 9 }\right) $.

Synthetic Division Calculator