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応用分野：組み立て除法の具体例，

組み立て除法と筆算の比較

$(2 x^{3} - 7 x^{2} + 7 x + 3) \div (x - 2)$ $(2 x^{3} - 7 x^{2} + 7 x + 3) \div (x - 2)$ の商と余りの計算の組み立て除法と筆算の比較

	組み立て除法	筆算
ステップ1	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \end{array}} \\ \begin{array}{l} \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \end{array}} \\ \begin{array}{l} \end{array} \end{array}$	$x - 2 \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3}$ $x - 2 \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3}$
ステップ2	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \end{array}} \\ \begin{array}{l} 2 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \end{array}} \\ \begin{array}{l} 2 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \end{array}$ $\begin{array}{l} 2 x^{2} \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \end{array}$
ステップ3	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 \end{array}} \\ \begin{array}{l} 2 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 \end{array}} \\ \begin{array}{l} 2 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ 2 x^{3} - 4 x^{2} \end{array}$ $\begin{array}{l} 2 x^{2} \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ 2 x^{3} - 4 x^{2} \end{array}$
ステップ4	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 \end{array}} \\ \begin{array}{l} 2 & - 3 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 \end{array}} \\ \begin{array}{l} 2 & - 3 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} - 3 x \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \end{array} \end{array}$ $\begin{array}{l} 2 x^{2} - 3 x \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \end{array} \end{array}$
ステップ5	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 \end{array}} \\ \begin{array}{l} 2 & - 3 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 \end{array}} \\ \begin{array}{l} 2 & - 3 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} - 3 x \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ - 3 x^{2} + 6 x \end{array} \end{array}$ $\begin{array}{l} 2 x^{2} - 3 x \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ - 3 x^{2} + 6 x \end{array} \end{array}$
ステップ6	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 \end{array}} \\ \begin{array}{l} 2 & - 3 & 1 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 \end{array}} \\ \begin{array}{l} 2 & - 3 & 1 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} - 3 x + 1 \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ \underline{- 3 x^{2} + 6 x} \\ x + 3 \end{array} \end{array}$ $\begin{array}{l} 2 x^{2} - 3 x + 1 \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ \underline{- 3 x^{2} + 6 x} \\ x + 3 \end{array} \end{array}$
ステップ7	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 & 2 \end{array}} \\ \begin{array}{l} 2 & - 3 & 1 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 & 2 \end{array}} \\ \begin{array}{l} 2 & - 3 & 1 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} - 3 x + 1 \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ \underline{- 3 x^{2} + 6 x} \\ x + 3 \\ x - 2 \end{array} \end{array}$ $\begin{array}{l} 2 x^{2} - 3 x + 1 \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ \underline{- 3 x^{2} + 6 x} \\ x + 3 \\ x - 2 \end{array} \end{array}$
ステップ8	$\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 & 2 \end{array}} \\ \begin{array}{l} 2 & - 3 & 1 & 5 \end{array} \end{array}$ $\begin{array}{l} \underline{\begin{array}{l} \underline{2 \|} & 2 & - 7 & 7 & 3 \\ 4 & - 6 & 2 \end{array}} \\ \begin{array}{l} 2 & - 3 & 1 & 5 \end{array} \end{array}$	$\begin{array}{l} 2 x^{2} - 3 x + 1 \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ \underline{- 3 x^{2} + 6 x} \\ x + 3 \\ \underline{x - 2} \\ 5 \end{array} \end{array}$ $\begin{array}{l} 2 x^{2} - 3 x + 1 \\ x - 2 & \bar{) 2 x^{3} - 7 x^{2} + 7 x + 3} \\ \begin{array}{l} \underline{2 x^{3} - 4 x^{2}} \\ - 3 x^{2} + 7 x \\ \underline{- 3 x^{2} + 6 x} \\ x + 3 \\ \underline{x - 2} \\ 5 \end{array} \end{array}$

ホーム>>カテゴリー別分類>>数と式>>組み立て除法>>組み立て除法の具体例>>組み立て除法と筆算の比較

最終更新日： 2024年6月26日

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