Find remainder when $ 4x^{3}+8x^{2}-3x-6 $ is divided by $ x+2 $.

The synthetic division table is:

$$ \begin{array}{c|rrrr}-2&4&8&-3&-6\\& & -8& 0& \color{black}{6} \\ \hline &\color{blue}{4}&\color{blue}{0}&\color{blue}{-3}&\color{orangered}{0} \end{array} $$

The remainder when $ 4x^{3}+8x^{2}-3x-6 $ is divided by $ x+2 $ is $ \, \color{red}{ 0 } $.

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 + 2 = 0 $ ( $ x = \color{blue}{ -2 } $ ) at the left.

$$ \begin{array}{c|rrrr}\color{blue}{-2}&4&8&-3&-6\\& & & & \\ \hline &&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}-2&\color{orangered}{ 4 }&8&-3&-6\\& & & & \\ \hline &\color{orangered}{4}&&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -2 } \cdot \color{blue}{ 4 } = \color{blue}{ -8 } $.

$$ \begin{array}{c|rrrr}\color{blue}{-2}&4&8&-3&-6\\& & \color{blue}{-8} & & \\ \hline &\color{blue}{4}&&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 8 } + \color{orangered}{ \left( -8 \right) } = \color{orangered}{ 0 } $

$$ \begin{array}{c|rrrr}-2&4&\color{orangered}{ 8 }&-3&-6\\& & \color{orangered}{-8} & & \\ \hline &4&\color{orangered}{0}&& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -2 } \cdot \color{blue}{ 0 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{-2}&4&8&-3&-6\\& & -8& \color{blue}{0} & \\ \hline &4&\color{blue}{0}&& \end{array} $$

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

$$ \begin{array}{c|rrrr}-2&4&8&\color{orangered}{ -3 }&-6\\& & -8& \color{orangered}{0} & \\ \hline &4&0&\color{orangered}{-3}& \end{array} $$

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

$$ \begin{array}{c|rrrr}\color{blue}{-2}&4&8&-3&-6\\& & -8& 0& \color{blue}{6} \\ \hline &4&0&\color{blue}{-3}& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ -6 } + \color{orangered}{ 6 } = \color{orangered}{ 0 } $

$$ \begin{array}{c|rrrr}-2&4&8&-3&\color{orangered}{ -6 }\\& & -8& 0& \color{orangered}{6} \\ \hline &\color{blue}{4}&\color{blue}{0}&\color{blue}{-3}&\color{orangered}{0} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ 0 }\right) $.

Synthetic Division Calculator