Divide using synthetic division $$ ( -36x^{2}-15x-16 ) \div ( -5 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrr}0&-36&-15&-16\\& & 0& \color{black}{0} \\ \hline &\color{blue}{-36}&\color{blue}{-15}&\color{orangered}{-16} \end{array} $$The solution is:
$$ \dfrac{ -36x^{2}-15x-16 }{ x } = \color{blue}{-36x-15} \color{red}{~-~} \dfrac{ \color{red}{ 16 } }{ x } $$Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.
$$ \begin{array}{c|rrr}\color{blue}{0}&-36&-15&-16\\& & & \\ \hline &&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrr}0&\color{orangered}{ -36 }&-15&-16\\& & & \\ \hline &\color{orangered}{-36}&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -36 \right) } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrr}\color{blue}{0}&-36&-15&-16\\& & \color{blue}{0} & \\ \hline &\color{blue}{-36}&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -15 } + \color{orangered}{ 0 } = \color{orangered}{ -15 } $
$$ \begin{array}{c|rrr}0&-36&\color{orangered}{ -15 }&-16\\& & \color{orangered}{0} & \\ \hline &-36&\color{orangered}{-15}& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -15 \right) } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrr}\color{blue}{0}&-36&-15&-16\\& & 0& \color{blue}{0} \\ \hline &-36&\color{blue}{-15}& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -16 } + \color{orangered}{ 0 } = \color{orangered}{ -16 } $
$$ \begin{array}{c|rrr}0&-36&-15&\color{orangered}{ -16 }\\& & 0& \color{orangered}{0} \\ \hline &\color{blue}{-36}&\color{blue}{-15}&\color{orangered}{-16} \end{array} $$Bottom line represents the quotient $ \color{blue}{ -36x-15 } $ with a remainder of $ \color{red}{ -16 } $.