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.

$$ \begin{array}{c|rrr}\color{blue}{4}&-14&13&23\\& & & \\ \hline &&& \end{array} $$

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

$$ \begin{array}{c|rrr}4&\color{orangered}{ -14 }&13&23\\& & & \\ \hline &\color{orangered}{-14}&& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 4 } \cdot \color{blue}{ \left( -14 \right) } = \color{blue}{ -56 } $.

$$ \begin{array}{c|rrr}\color{blue}{4}&-14&13&23\\& & \color{blue}{-56} & \\ \hline &\color{blue}{-14}&& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 13 } + \color{orangered}{ \left( -56 \right) } = \color{orangered}{ -43 } $

$$ \begin{array}{c|rrr}4&-14&\color{orangered}{ 13 }&23\\& & \color{orangered}{-56} & \\ \hline &-14&\color{orangered}{-43}& \end{array} $$

Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 4 } \cdot \color{blue}{ \left( -43 \right) } = \color{blue}{ -172 } $.

$$ \begin{array}{c|rrr}\color{blue}{4}&-14&13&23\\& & -56& \color{blue}{-172} \\ \hline &-14&\color{blue}{-43}& \end{array} $$

Step 5 : Add down last column: $ \color{orangered}{ 23 } + \color{orangered}{ \left( -172 \right) } = \color{orangered}{ -149 } $

$$ \begin{array}{c|rrr}4&-14&13&\color{orangered}{ 23 }\\& & -56& \color{orangered}{-172} \\ \hline &\color{blue}{-14}&\color{blue}{-43}&\color{orangered}{-149} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ -14x-43 } $ with a remainder of $ \color{red}{ -149 } $.

Synthetic Division Calculator