Find remainder when $ -3x^{3}-4x^{2}+7x-2 $ is divided by $ 2 $.

The synthetic division table is:

$$ \begin{array}{c|rrrr}0&-3&-4&7&-2\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{-3}&\color{blue}{-4}&\color{blue}{7}&\color{orangered}{-2} \end{array} $$

The remainder when $ -3x^{3}-4x^{2}+7x-2 $ is divided by $ x $ is $ \, \color{red}{ -2 } $.

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.

$$ \begin{array}{c|rrrr}\color{blue}{0}&-3&-4&7&-2\\& & & & \\ \hline &&&& \end{array} $$

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

$$ \begin{array}{c|rrrr}0&\color{orangered}{ -3 }&-4&7&-2\\& & & & \\ \hline &\color{orangered}{-3}&&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -3 \right) } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&-3&-4&7&-2\\& & \color{blue}{0} & & \\ \hline &\color{blue}{-3}&&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -4 } + \color{orangered}{ 0 } = \color{orangered}{ -4 } $

$$ \begin{array}{c|rrrr}0&-3&\color{orangered}{ -4 }&7&-2\\& & \color{orangered}{0} & & \\ \hline &-3&\color{orangered}{-4}&& \end{array} $$

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

$$ \begin{array}{c|rrrr}\color{blue}{0}&-3&-4&7&-2\\& & 0& \color{blue}{0} & \\ \hline &-3&\color{blue}{-4}&& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ 7 } + \color{orangered}{ 0 } = \color{orangered}{ 7 } $

$$ \begin{array}{c|rrrr}0&-3&-4&\color{orangered}{ 7 }&-2\\& & 0& \color{orangered}{0} & \\ \hline &-3&-4&\color{orangered}{7}& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 7 } = \color{blue}{ 0 } $.

$$ \begin{array}{c|rrrr}\color{blue}{0}&-3&-4&7&-2\\& & 0& 0& \color{blue}{0} \\ \hline &-3&-4&\color{blue}{7}& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ -2 } + \color{orangered}{ 0 } = \color{orangered}{ -2 } $

$$ \begin{array}{c|rrrr}0&-3&-4&7&\color{orangered}{ -2 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{-3}&\color{blue}{-4}&\color{blue}{7}&\color{orangered}{-2} \end{array} $$

Remainder is the last entry in the bottom row $ \left(\color{red}{ -2 }\right) $.

Synthetic Division Calculator