Find remainder when $ -2x^{2}-10x-9 $ is divided by $ x+3 $.

The synthetic division table is:

$$ \begin{array}{c|rrr}-3&-2&-10&-9\\& & 6& \color{black}{12} \\ \hline &\color{blue}{-2}&\color{blue}{-4}&\color{orangered}{3} \end{array} $$

The remainder when $ -2x^{2}-10x-9 $ is divided by $ x+3 $ is $ \, \color{red}{ 3 } $.

We can find remainder using synthetic division method.

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 3 = 0 $ ( $ x = \color{blue}{ -3 } $ ) at the left.

$$ \begin{array}{c|rrr}\color{blue}{-3}&-2&-10&-9\\& & & \\ \hline &&& \end{array} $$

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

$$ \begin{array}{c|rrr}-3&\color{orangered}{ -2 }&-10&-9\\& & & \\ \hline &\color{orangered}{-2}&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -3 } \cdot \color{blue}{ \left( -2 \right) } = \color{blue}{ 6 } $.

$$ \begin{array}{c|rrr}\color{blue}{-3}&-2&-10&-9\\& & \color{blue}{6} & \\ \hline &\color{blue}{-2}&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -10 } + \color{orangered}{ 6 } = \color{orangered}{ -4 } $

$$ \begin{array}{c|rrr}-3&-2&\color{orangered}{ -10 }&-9\\& & \color{orangered}{6} & \\ \hline &-2&\color{orangered}{-4}& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -3 } \cdot \color{blue}{ \left( -4 \right) } = \color{blue}{ 12 } $.

$$ \begin{array}{c|rrr}\color{blue}{-3}&-2&-10&-9\\& & 6& \color{blue}{12} \\ \hline &-2&\color{blue}{-4}& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ -9 } + \color{orangered}{ 12 } = \color{orangered}{ 3 } $

$$ \begin{array}{c|rrr}-3&-2&-10&\color{orangered}{ -9 }\\& & 6& \color{orangered}{12} \\ \hline &\color{blue}{-2}&\color{blue}{-4}&\color{orangered}{3} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 3 }\right) $.

Synthetic Division Calculator