Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 19 = 0 $ ( $ x = \color{blue}{ -19 } $ ) at the left.

$$ \begin{array}{c|rrrrrr}\color{blue}{-19}&2&-4&2&0&-1&9\\& & & & & & \\ \hline &&&&&& \end{array} $$

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

$$ \begin{array}{c|rrrrrr}-19&\color{orangered}{ 2 }&-4&2&0&-1&9\\& & & & & & \\ \hline &\color{orangered}{2}&&&&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -19 } \cdot \color{blue}{ 2 } = \color{blue}{ -38 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-19}&2&-4&2&0&-1&9\\& & \color{blue}{-38} & & & & \\ \hline &\color{blue}{2}&&&&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ -4 } + \color{orangered}{ \left( -38 \right) } = \color{orangered}{ -42 } $

$$ \begin{array}{c|rrrrrr}-19&2&\color{orangered}{ -4 }&2&0&-1&9\\& & \color{orangered}{-38} & & & & \\ \hline &2&\color{orangered}{-42}&&&& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -19 } \cdot \color{blue}{ \left( -42 \right) } = \color{blue}{ 798 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-19}&2&-4&2&0&-1&9\\& & -38& \color{blue}{798} & & & \\ \hline &2&\color{blue}{-42}&&&& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ 2 } + \color{orangered}{ 798 } = \color{orangered}{ 800 } $

$$ \begin{array}{c|rrrrrr}-19&2&-4&\color{orangered}{ 2 }&0&-1&9\\& & -38& \color{orangered}{798} & & & \\ \hline &2&-42&\color{orangered}{800}&&& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -19 } \cdot \color{blue}{ 800 } = \color{blue}{ -15200 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-19}&2&-4&2&0&-1&9\\& & -38& 798& \color{blue}{-15200} & & \\ \hline &2&-42&\color{blue}{800}&&& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -15200 \right) } = \color{orangered}{ -15200 } $

$$ \begin{array}{c|rrrrrr}-19&2&-4&2&\color{orangered}{ 0 }&-1&9\\& & -38& 798& \color{orangered}{-15200} & & \\ \hline &2&-42&800&\color{orangered}{-15200}&& \end{array} $$

Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -19 } \cdot \color{blue}{ \left( -15200 \right) } = \color{blue}{ 288800 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-19}&2&-4&2&0&-1&9\\& & -38& 798& -15200& \color{blue}{288800} & \\ \hline &2&-42&800&\color{blue}{-15200}&& \end{array} $$

Step 9 : Add down last column: $ \color{orangered}{ -1 } + \color{orangered}{ 288800 } = \color{orangered}{ 288799 } $

$$ \begin{array}{c|rrrrrr}-19&2&-4&2&0&\color{orangered}{ -1 }&9\\& & -38& 798& -15200& \color{orangered}{288800} & \\ \hline &2&-42&800&-15200&\color{orangered}{288799}& \end{array} $$

Step 10 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -19 } \cdot \color{blue}{ 288799 } = \color{blue}{ -5487181 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-19}&2&-4&2&0&-1&9\\& & -38& 798& -15200& 288800& \color{blue}{-5487181} \\ \hline &2&-42&800&-15200&\color{blue}{288799}& \end{array} $$

Step 11 : Add down last column: $ \color{orangered}{ 9 } + \color{orangered}{ \left( -5487181 \right) } = \color{orangered}{ -5487172 } $

$$ \begin{array}{c|rrrrrr}-19&2&-4&2&0&-1&\color{orangered}{ 9 }\\& & -38& 798& -15200& 288800& \color{orangered}{-5487181} \\ \hline &\color{blue}{2}&\color{blue}{-42}&\color{blue}{800}&\color{blue}{-15200}&\color{blue}{288799}&\color{orangered}{-5487172} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 2x^{4}-42x^{3}+800x^{2}-15200x+288799 } $ with a remainder of $ \color{red}{ -5487172 } $.

Synthetic Division Calculator