次の式を因数分解しよう。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\S{x+y} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & (\colBX{bisque}{$\S$}-2)(\colBX{bisque}{$\S$}+4)+5\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=(A-2)(A+4)+5\\ &\color{gray}=(A^2+2A-8)+5\\ &\color{gray}=A^2+2A-3\\ & \colMM{red}{ A=\S\ に戻す}\\ &=(\colBX{bisque}{$\S$})^2+2(\colBX{bisque}{$\S$})-3\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=A^2+2A-3\\ &\color{gray}=(A+3)(A-1)\\ & \colMM{red}{ A=\S\ に戻す}\\ &= \left\{(\colBX{bisque}{$\S$})+3\right\}\left\{(\colBX{bisque}{$\S$})-1\right\}\\ \\ &= (\S+3)(\S-1) \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)
【解答】
\def\S{x+2y} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & (\colBX{bisque}{$\S$}+1)(\colBX{bisque}{$\S$}-2)-4\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=(A+1)(A-2)-4\\ &\color{gray}=(A^2-A-2)-4\\ &\color{gray}=A^2-A-6\\ & \colMM{red}{ A=\S\ に戻す}\\ &=(\colBX{bisque}{$\S$})^2-(\colBX{bisque}{$\S$})-6\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=A^2-A-6\\ &\color{gray}=(A+2)(A-3)\\ & \colMM{red}{ A=\S\ に戻す}\\ &= \left\{(\colBX{bisque}{$\S$})+2\right\}\left\{(\colBX{bisque}{$\S$})-3\right\}\\ \\ &= (\S+2)(\S-3) \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)
【解答】
\def\S{x+2y} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & (\colBX{bisque}{$\S$}-2z)(\colBX{bisque}{$\S$}-3z)-12z^2\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=(A-2z)(A-3z)-12z^2\\ &\color{gray}=(A^2-5Az+6z^2)-12z^2\\ &\color{gray}=A^2-5Az-6z^2\\ & \colMM{red}{ A=\S\ に戻す}\\ &=(\colBX{bisque}{$\S$})^2-5(\colBX{bisque}{$\S$})z-6z^2\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=A^2-5Az-6z^2\\ &\color{gray}=(A+z)(A-6z)\\ & \colMM{red}{ A=\S\ に戻す}\\ &= \left\{(\colBX{bisque}{$\S$})+z\right\}\left\{(\colBX{bisque}{$\S$})-6z\right\}\\ \\ &= (\S+z)(\S-6z) \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan
次の式を因数分解しよう。
↓この問題へのリンクはこちら(右クリックで保存)
【解答】
\def\S{x^2} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & x^4-13x^2+36\\ \\ &= (\colBX{bisque}{$\S$})^2-13\colBX{bisque}{$\S$}+36\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=A^2-13A+36\\ &\color{gray}=(A-4)(A-9)\\ & \colMM{red}{ A=\S\ に戻す}\\ &=(\colBX{bisque}{$\S$}-4)(\colBX{bisque}{$\S$}-9)\\ \\ &\color{lightgray}=(\S-2^2)(\S-3^2)\\ \\ &= (x+2)(x-2)(x+3)(x-3) \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)
【解答】
\def\S{x^2} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & x^4-5x^2+4\\ \\ &= (\colBX{bisque}{$\S$})^2-5\colBX{bisque}{$\S$}+4\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=A^2-5A+4\\ &\color{gray}=(A-1)(A-4)\\ & \colMM{red}{ A=\S\ に戻す}\\ &=(\colBX{bisque}{$\S$}-1)(\colBX{bisque}{$\S$}-4)\\ \\ &\color{lightgray}=(\S-1^2)(\S-2^2)\\ \\ &= (x+1)(x-1)(x+2)(x-2) \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)
【解答】
\def\S{x^2} \newcommand\colNS[2]{\color{#1}#2\color{black}} \newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\color{#1}\scriptsize #2\color{black}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}} \begin{align*} & x^4-17x^2+16\\ \\ &= (\colBX{bisque}{$\S$})^2-17\colBX{bisque}{$\S$}+16\\ & \colMM{red}{ 同じパーツ➡\S=Aとおく}\\ &\color{gray}=A^2-17A+16\\ &\color{gray}=(A-1)(A-16)\\ & \colMM{red}{ A=\S\ に戻す}\\ &=(\colBX{bisque}{$\S$}-1)(\colBX{bisque}{$\S$}-16)\\ \\ &\color{lightgray}=(\S-1^2)(\S-4^2)\\ \\ &= (x+1)(x-1)(x+4)(x-4) \end{align*} %1 orange,bisque %2 green,palegreen %3 magenta, violet %4 deepskyblue, lightcyan