32022中３・多項式の因数分解・計算問題・因数分解の公式1-2

(1) $\quad\;\,\begin{eqnarray}x^{2}-2x-8\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}+ \color{red}\{(+2)+(-4)\} \color{black}x+\color{red}\{(+2) \times (-4)\} \\[6pt]&=&(\,x+2\,)(\,x-4\,)\end{eqnarray}\;\;$

答$(\,x+2\,)(\,x-4\,)$

(2) $\quad\;\,\begin{eqnarray}x^{2}-x-6\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}+ \color{red}\{(+2)+(-3)\} \color{black}x+\color{red}\{(+2) \times (-3)\} \\[6pt]&=&(\,x+2\,)(\,x-3\,)\end{eqnarray}\;\;$

答$(\,x+2\,)(\,x-3\,)$

(3) $\quad\;\,\begin{eqnarray}x^{2}+4x-12\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}+ \color{red}\{(+6)+(-2)\} \color{black}x+\color{red}\{(+6) \times (-2)\} \\[6pt]&=&(\,x+6\,)(\,x-2\,)\end{eqnarray}\;\;$

答$(\,x+6\,)(\,x-2\,)$

(4) $\quad\;\,\begin{eqnarray}x^{2}-2x-48\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}+ \color{red}\{(+6)+(-8)\} \color{black}x+ \color{red}\{(+6) \times (-8)\} \\[6pt]&=&(\,x+6\,)(\,x-8\,)\end{eqnarray}\;\;$

答$(\,x+6\,)(\,x-8\,)$

(5) $\quad\;\,\begin{eqnarray}x^{2}+9x-36\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}+ \color{red}\{(+12)+(-3)\} \color{black}x+ \color{red}\{(+12) \times (-3)\} \\[6pt]&=&(\,x+12\,)(\,x-3\,)\end{eqnarray}\;\;$

答$(\,x+12\,)(\,x-3\,)$

(6) $\quad\;\,\begin{eqnarray}x^{2}-12x-64\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}+ \color{red}\{(\,+4\,)+(\,-16\,)\} \color{black}x+ \color{red}\{(\,+4\,) \times (\,-16\,)\}\\[6pt]&=&(\,x+4\,)(\,x-16\,)\end{eqnarray}\;\;$

答$(\,x+4\,)(\,x-16\,)$