割られる式 A を求めよう
次の条件を満たす整式 A を求めよ。
↓この問題へのリンクはこちら(右クリックで保存)
\newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colBX{bisque}{$A$}\ を &\ \colBX{palegreen}{$B$}\ で割ると,商が\ \colBX{violet}{$Q$},余りが\ \colBX{lightcyan}{$R$}\\ \\ & \colNS{red}{\Darr\ 4つの要素がそろった!}\\ \\ \Large \colBX{bisque}{$A$} & \Large = \colBX{palegreen}{$B$} \times \colBX{violet}{$Q$} + \colBX{lightcyan}{$R$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】
\def\B{x-1} \def\Q{x^2-x+1} \def\R{5} \def\Tenkai{x^3-x^2+x-x^2+x-1} \def\Kotae{x^3-2x^2+2x+4} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} 整式 & \ \colBX{bisque}{$A$}\ を \ \colBX{palegreen}{$\B$}\ で割ると,\\ & 商が\ \colBX{violet}{$\Q$},余りが\ \colBX{lightcyan}{$\R$}\ であるから\\ \\ \colBX{bisque}{$A$} = & (\colBX{palegreen}{$\B$})(\colBX{violet}{$\Q$})+\colBX{lightcyan}{$\R$}\\ \\ = & \Tenkai +\R\\ \\ = & \Kotae \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
\newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colBX{bisque}{$A$}\ を &\ \colBX{palegreen}{$B$}\ で割ると,商が\ \colBX{violet}{$Q$},余りが\ \colBX{lightcyan}{$R$}\\ \\ & \colNS{red}{\Darr\ 4つの要素がそろった!}\\ \\ \Large \colBX{bisque}{$A$} & \Large = \colBX{palegreen}{$B$} \times \colBX{violet}{$Q$} + \colBX{lightcyan}{$R$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】
\def\B{x+2} \def\Q{x+3} \def\R{-1} \def\Tenkai{x^2+5x+6} \def\Kotae{x^2+5x+5} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} 整式 & \ \colBX{bisque}{$A$}\ を \ \colBX{palegreen}{$\B$}\ で割ると,\\ & 商が\ \colBX{violet}{$\Q$},余りが\ \colBX{lightcyan}{$\R$}\ であるから\\ \\ \colBX{bisque}{$A$} = & (\colBX{palegreen}{$\B$})(\colBX{violet}{$\Q$})\colBX{lightcyan}{$\R$}\\ \\ = & \Tenkai \R\\ \\ = & \Kotae \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
↓この問題へのリンクはこちら(右クリックで保存)
\newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} \colBX{bisque}{$A$}\ を &\ \colBX{palegreen}{$B$}\ で割ると,商が\ \colBX{violet}{$Q$},余りが\ \colBX{lightcyan}{$R$}\\ \\ & \colNS{red}{\Darr\ 4つの要素がそろった!}\\ \\ \Large \colBX{bisque}{$A$} & \Large = \colBX{palegreen}{$B$} \times \colBX{violet}{$Q$} + \colBX{lightcyan}{$R$} \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
【解答】
\def\B{x^2+2x+3} \def\Q{x-1} \def\R{2x+3} \def\Tenkai{x^3-x^2+2x^2-2x+3x-3} \def\Kotae{x^3+x^2+3x} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} 整式 & \ \colBX{bisque}{$A$}\ を \ \colBX{palegreen}{$\B$}\ で割ると,\\ & 商が\ \colBX{violet}{$\Q$},余りが\ \colBX{lightcyan}{$\R$}\ であるから\\ \\ \colBX{bisque}{$A$} = & (\colBX{palegreen}{$\B$})(\colBX{violet}{$\Q$}) + \colBX{lightcyan}{$\R$}\\ \\ = & \Tenkai + \R\\ \\ = & \Kotae \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan