Divide using synthetic division $$ ( 18x^{4}-60x^{2}-48 ) \div ( 2x+4 ) $$
The synthetic division table is:
$$ \begin{array}{c|rrrrr}-4&18&0&-60&0&-48\\& & -72& 288& -912& \color{black}{3648} \\ \hline &\color{blue}{18}&\color{blue}{-72}&\color{blue}{228}&\color{blue}{-912}&\color{orangered}{3600} \end{array} $$The solution is:
$$ \dfrac{ 18x^{4}-60x^{2}-48 }{ x+4 } = \color{blue}{18x^{3}-72x^{2}+228x-912} ~+~ \dfrac{ \color{red}{ 3600 } }{ x+4 } $$Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 4 = 0 $ ( $ x = \color{blue}{ -4 } $ ) at the left.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&18&0&-60&0&-48\\& & & & & \\ \hline &&&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrrr}-4&\color{orangered}{ 18 }&0&-60&0&-48\\& & & & & \\ \hline &\color{orangered}{18}&&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 18 } = \color{blue}{ -72 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&18&0&-60&0&-48\\& & \color{blue}{-72} & & & \\ \hline &\color{blue}{18}&&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -72 \right) } = \color{orangered}{ -72 } $
$$ \begin{array}{c|rrrrr}-4&18&\color{orangered}{ 0 }&-60&0&-48\\& & \color{orangered}{-72} & & & \\ \hline &18&\color{orangered}{-72}&&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ \left( -72 \right) } = \color{blue}{ 288 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&18&0&-60&0&-48\\& & -72& \color{blue}{288} & & \\ \hline &18&\color{blue}{-72}&&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -60 } + \color{orangered}{ 288 } = \color{orangered}{ 228 } $
$$ \begin{array}{c|rrrrr}-4&18&0&\color{orangered}{ -60 }&0&-48\\& & -72& \color{orangered}{288} & & \\ \hline &18&-72&\color{orangered}{228}&& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 228 } = \color{blue}{ -912 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&18&0&-60&0&-48\\& & -72& 288& \color{blue}{-912} & \\ \hline &18&-72&\color{blue}{228}&& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ 0 } + \color{orangered}{ \left( -912 \right) } = \color{orangered}{ -912 } $
$$ \begin{array}{c|rrrrr}-4&18&0&-60&\color{orangered}{ 0 }&-48\\& & -72& 288& \color{orangered}{-912} & \\ \hline &18&-72&228&\color{orangered}{-912}& \end{array} $$Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ \left( -912 \right) } = \color{blue}{ 3648 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&18&0&-60&0&-48\\& & -72& 288& -912& \color{blue}{3648} \\ \hline &18&-72&228&\color{blue}{-912}& \end{array} $$Step 9 : Add down last column: $ \color{orangered}{ -48 } + \color{orangered}{ 3648 } = \color{orangered}{ 3600 } $
$$ \begin{array}{c|rrrrr}-4&18&0&-60&0&\color{orangered}{ -48 }\\& & -72& 288& -912& \color{orangered}{3648} \\ \hline &\color{blue}{18}&\color{blue}{-72}&\color{blue}{228}&\color{blue}{-912}&\color{orangered}{3600} \end{array} $$Bottom line represents the quotient $ \color{blue}{ 18x^{3}-72x^{2}+228x-912 } $ with a remainder of $ \color{red}{ 3600 } $.