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.

$$ \begin{array}{c|rrrrrr}\color{blue}{3}&-1&1&0&0&16&-16\\& & & & & & \\ \hline &&&&&& \end{array} $$

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

$$ \begin{array}{c|rrrrrr}3&\color{orangered}{ -1 }&1&0&0&16&-16\\& & & & & & \\ \hline &\color{orangered}{-1}&&&&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -1 \right) } = \color{blue}{ -3 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{3}&-1&1&0&0&16&-16\\& & \color{blue}{-3} & & & & \\ \hline &\color{blue}{-1}&&&&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 1 } + \color{orangered}{ \left( -3 \right) } = \color{orangered}{ -2 } $

$$ \begin{array}{c|rrrrrr}3&-1&\color{orangered}{ 1 }&0&0&16&-16\\& & \color{orangered}{-3} & & & & \\ \hline &-1&\color{orangered}{-2}&&&& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -2 \right) } = \color{blue}{ -6 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{3}&-1&1&0&0&16&-16\\& & -3& \color{blue}{-6} & & & \\ \hline &-1&\color{blue}{-2}&&&& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -6 \right) } = \color{orangered}{ -6 } $

$$ \begin{array}{c|rrrrrr}3&-1&1&\color{orangered}{ 0 }&0&16&-16\\& & -3& \color{orangered}{-6} & & & \\ \hline &-1&-2&\color{orangered}{-6}&&& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -6 \right) } = \color{blue}{ -18 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{3}&-1&1&0&0&16&-16\\& & -3& -6& \color{blue}{-18} & & \\ \hline &-1&-2&\color{blue}{-6}&&& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -18 \right) } = \color{orangered}{ -18 } $

$$ \begin{array}{c|rrrrrr}3&-1&1&0&\color{orangered}{ 0 }&16&-16\\& & -3& -6& \color{orangered}{-18} & & \\ \hline &-1&-2&-6&\color{orangered}{-18}&& \end{array} $$

Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -18 \right) } = \color{blue}{ -54 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{3}&-1&1&0&0&16&-16\\& & -3& -6& -18& \color{blue}{-54} & \\ \hline &-1&-2&-6&\color{blue}{-18}&& \end{array} $$

Step 9 : Add down last column: $ \color{orangered}{ 16 } + \color{orangered}{ \left( -54 \right) } = \color{orangered}{ -38 } $

$$ \begin{array}{c|rrrrrr}3&-1&1&0&0&\color{orangered}{ 16 }&-16\\& & -3& -6& -18& \color{orangered}{-54} & \\ \hline &-1&-2&-6&-18&\color{orangered}{-38}& \end{array} $$

Step 10 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 3 } \cdot \color{blue}{ \left( -38 \right) } = \color{blue}{ -114 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{3}&-1&1&0&0&16&-16\\& & -3& -6& -18& -54& \color{blue}{-114} \\ \hline &-1&-2&-6&-18&\color{blue}{-38}& \end{array} $$

Step 11 : Add down last column: $ \color{orangered}{ -16 } + \color{orangered}{ \left( -114 \right) } = \color{orangered}{ -130 } $

$$ \begin{array}{c|rrrrrr}3&-1&1&0&0&16&\color{orangered}{ -16 }\\& & -3& -6& -18& -54& \color{orangered}{-114} \\ \hline &\color{blue}{-1}&\color{blue}{-2}&\color{blue}{-6}&\color{blue}{-18}&\color{blue}{-38}&\color{orangered}{-130} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -x^{4}-2x^{3}-6x^{2}-18x-38 } $ with a remainder of $ \color{red}{ -130 } $.

Synthetic Division Calculator