組立除法の具体例

$3$\displaystyle{ $ 2{x}^{3}- 7{x}^{2}+7x+3 $ \div $ x- 2 $ }$ の商と余りを組立除法で求める．

ステップ1	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{B} &\text{D}&\text{F}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}\text{A} & \text{\hspace{1}}\text{C} & \text{\hspace{1}}\text{E} & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{ x- 2 }$ で割る場合，左上端に2を記入し　＿｜　で囲む． $3$\displaystyle{ 2{x}^{3}- 7{x}^{2}+7x+3 }$ の各次数の項の係数と定数項と右隣りに記入する．以下のステップでA，B，C，D，E，F，Gの順に数値を記入していく．
ステップ2	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{B} &\text{D}&\text{F}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & \text{\hspace{1}}\text{C} & \text{\hspace{1}}\text{E} & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	最高次数の $3$\displaystyle{ {x}^{3} }$ の係数の2をAのところに記入する．
ステップ3	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &\text{D}&\text{F}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & \text{\hspace{1}}\text{C} & \text{\hspace{1}}\text{E} & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	左上端の2とAのところに記入した2をかけた値をBのところに記入する．
ステップ4	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &\text{D}&\text{F}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}\text{E} & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{ {x}^{2} }$ の係数の－7とBのところに記入した4の和をCのところに記入する．
ステップ5	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&\text{F}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}\text{E} & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	左上端の2とCのところに記入した－3をかけた値をDのところに記入する．
ステップ6	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&\text{F}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}1 & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$x$ の係数の7とDのところに記入した－6の和をEのところに記入する．
ステップ7	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&2& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}1 & \text{\hspace{1}}\text{G} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	左上端の2とEのところに記入した1をかけた値をFのところに記入する．
ステップ8	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&2& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}1 & \text{\hspace{1}}5 & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	定数項の3とFのところに記入した2の和をGのところに記入する．