Divide using synthetic division $$ ( 18x^{3}+15x^{2}-x-2 ) \div ( -2 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrrr}0&18&15&-1&-2\\& & 0& 0& \color{black}{0} \\ \hline &\color{blue}{18}&\color{blue}{15}&\color{blue}{-1}&\color{orangered}{-2} \end{array} $$The solution is:
$$ \dfrac{ 18x^{3}+15x^{2}-x-2 }{ x } = \color{blue}{18x^{2}+15x-1} \color{red}{~-~} \dfrac{ \color{red}{ 2 } }{ x } $$Step 1 : Write down the coefficients of the dividend into division table.Put the zero at the left.
$$ \begin{array}{c|rrrr}\color{blue}{0}&18&15&-1&-2\\& & & & \\ \hline &&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrr}0&\color{orangered}{ 18 }&15&-1&-2\\& & & & \\ \hline &\color{orangered}{18}&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 18 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&18&15&-1&-2\\& & \color{blue}{0} & & \\ \hline &\color{blue}{18}&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 15 } + \color{orangered}{ 0 } = \color{orangered}{ 15 } $
$$ \begin{array}{c|rrrr}0&18&\color{orangered}{ 15 }&-1&-2\\& & \color{orangered}{0} & & \\ \hline &18&\color{orangered}{15}&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ 15 } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&18&15&-1&-2\\& & 0& \color{blue}{0} & \\ \hline &18&\color{blue}{15}&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -1 } + \color{orangered}{ 0 } = \color{orangered}{ -1 } $
$$ \begin{array}{c|rrrr}0&18&15&\color{orangered}{ -1 }&-2\\& & 0& \color{orangered}{0} & \\ \hline &18&15&\color{orangered}{-1}& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 0 } \cdot \color{blue}{ \left( -1 \right) } = \color{blue}{ 0 } $.
$$ \begin{array}{c|rrrr}\color{blue}{0}&18&15&-1&-2\\& & 0& 0& \color{blue}{0} \\ \hline &18&15&\color{blue}{-1}& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ -2 } + \color{orangered}{ 0 } = \color{orangered}{ -2 } $
$$ \begin{array}{c|rrrr}0&18&15&-1&\color{orangered}{ -2 }\\& & 0& 0& \color{orangered}{0} \\ \hline &\color{blue}{18}&\color{blue}{15}&\color{blue}{-1}&\color{orangered}{-2} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 18x^{2}+15x-1 } $ with a remainder of $ \color{red}{ -2 } $.