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

$$ \begin{array}{c|rrrrrr}\color{blue}{-1}&32&0&-16&0&0&-5\\& & & & & & \\ \hline &&&&&& \end{array} $$

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

$$ \begin{array}{c|rrrrrr}-1&\color{orangered}{ 32 }&0&-16&0&0&-5\\& & & & & & \\ \hline &\color{orangered}{32}&&&&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ 32 } = \color{blue}{ -32 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-1}&32&0&-16&0&0&-5\\& & \color{blue}{-32} & & & & \\ \hline &\color{blue}{32}&&&&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -32 \right) } = \color{orangered}{ -32 } $

$$ \begin{array}{c|rrrrrr}-1&32&\color{orangered}{ 0 }&-16&0&0&-5\\& & \color{orangered}{-32} & & & & \\ \hline &32&\color{orangered}{-32}&&&& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ \left( -32 \right) } = \color{blue}{ 32 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-1}&32&0&-16&0&0&-5\\& & -32& \color{blue}{32} & & & \\ \hline &32&\color{blue}{-32}&&&& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ -16 } + \color{orangered}{ 32 } = \color{orangered}{ 16 } $

$$ \begin{array}{c|rrrrrr}-1&32&0&\color{orangered}{ -16 }&0&0&-5\\& & -32& \color{orangered}{32} & & & \\ \hline &32&-32&\color{orangered}{16}&&& \end{array} $$

Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ 16 } = \color{blue}{ -16 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-1}&32&0&-16&0&0&-5\\& & -32& 32& \color{blue}{-16} & & \\ \hline &32&-32&\color{blue}{16}&&& \end{array} $$

Step 7 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -16 \right) } = \color{orangered}{ -16 } $

$$ \begin{array}{c|rrrrrr}-1&32&0&-16&\color{orangered}{ 0 }&0&-5\\& & -32& 32& \color{orangered}{-16} & & \\ \hline &32&-32&16&\color{orangered}{-16}&& \end{array} $$

Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ \left( -16 \right) } = \color{blue}{ 16 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-1}&32&0&-16&0&0&-5\\& & -32& 32& -16& \color{blue}{16} & \\ \hline &32&-32&16&\color{blue}{-16}&& \end{array} $$

Step 9 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ 16 } = \color{orangered}{ 16 } $

$$ \begin{array}{c|rrrrrr}-1&32&0&-16&0&\color{orangered}{ 0 }&-5\\& & -32& 32& -16& \color{orangered}{16} & \\ \hline &32&-32&16&-16&\color{orangered}{16}& \end{array} $$

Step 10 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -1 } \cdot \color{blue}{ 16 } = \color{blue}{ -16 } $.

$$ \begin{array}{c|rrrrrr}\color{blue}{-1}&32&0&-16&0&0&-5\\& & -32& 32& -16& 16& \color{blue}{-16} \\ \hline &32&-32&16&-16&\color{blue}{16}& \end{array} $$

Step 11 : Add down last column: $ \color{orangered}{ -5 } + \color{orangered}{ \left( -16 \right) } = \color{orangered}{ -21 } $

$$ \begin{array}{c|rrrrrr}-1&32&0&-16&0&0&\color{orangered}{ -5 }\\& & -32& 32& -16& 16& \color{orangered}{-16} \\ \hline &\color{blue}{32}&\color{blue}{-32}&\color{blue}{16}&\color{blue}{-16}&\color{blue}{16}&\color{orangered}{-21} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 32x^{4}-32x^{3}+16x^{2}-16x+16 } $ with a remainder of $ \color{red}{ -21 } $.

Synthetic Division Calculator