【新課程】数研出版：新編数学Ⅰ[714]

p.8 練習1\({\small (1)}~\)係数 \(6\)、次数 \(2\)
\({\small (2)}~\)係数 \(1\)、次数 \(1\)
\({\small (3)}~\)係数 \(-1\)、次数 \(4\)
\({\small (4)}~\)係数 \(-3\)、次数 \(3\)

p.8 練習2\({\small (1)}~\)係数 \(2a\)、次数 \(3\)
\({\small (2)}~\)係数 \(3bc^3\) 次数 \(2\)
\({\small (3)}~\)係数 \(-6a\) 次数 \(3\)
→ 単項式の次数と係数

p.9 練習3$${\small (1)}~2x^2-x+5$$$${\small (2)}~-2a^2-12b^2$$

p.9 練習4\({\small (1)}~\)３次式
\({\small (2)}~\)４次式

p.10 練習5\({\small (1)}~\)３次式、定数項 \(by^2+c\)
\({\small (2)}~\)２次式、定数項 \(ax^3+c\)
→ 多項式の次数と定数項

p.10 練習6$${\small (1)}~(a+2)x+(4a^2-3a)$$$${\small (2)}~x^2+(3y-1)x+(2y^2-3y-2)$$

p.11 練習7$${\small (1)}~{\rm A+B}=6x^2-2x-7$$$$~~~~~~ {\rm A-B}=-2x^2+8x+5$$$${\small (2)}~{\rm A+B}=6x^3-6x^2-2x+12$$$$~~~~~~ {\rm A-B}=2x^3-2x-2$$

p.11 練習8$${\small (1)}~5x^2+2x+5$$$${\small (2)}~-4x^2+11x-18$$→ 多項式の計算

p.12 練習9$${\small (1)}~8a^5$$$${\small (2)}~-3a^3$$$${\small (3)}~4ab^6$$$${\small (4)}~-6x^5y^3$$$${\small (5)}~a^4b^6$$$${\small (6)}~-27x^6y^3$$→ 累乗の計算

p.13 練習10$${\small (1)}~8x^4-12x^3+20x^2$$$${\small (2)}~-6a^3+2a^2+4a$$

p.13 練習11$${\small (1)}~8x^3-4x^2+6x-3$$$${\small (2)}~2x^3-3x^2-5x+6$$$${\small (3)}~x^3+x^2-5x+3$$$${\small (4)}~6x^3+5x^2y-3xy^2-2y^3$$

p.14 練習12$${\small (1)}~9x^2+30x+25$$$${\small (2)}~4x^2-12xy+9y^2$$$${\small (3)}~x^2-36$$$${\small (4)}~25x^2-16y^2$$$${\small (5)}~x^2+6x+5$$$${\small (6)}~x^2+5x-24$$$${\small (7)}~x^2-6x+8$$$${\small (8)}~x^2+7xy+10y^2$$$${\small (9)}~x^2-4ax-21a^2$$→ 分配法則と展開

p.15 練習13$${\small (1)}~8x^2+14x+5$$$${\small (2)}~2x^2+5x-12$$$${\small (3)}~3x^2-x-14$$$${\small (4)}~4x^2-12x+5$$$${\small (5)}~3x^2+5xy-2y^2$$$${\small (6)}~12x^2-17ax+6a^2$$
→ ２次式の展開と乗法公式

p.15 練習14$${\small (1)}~9a^2-6ab+b^2-4$$$${\small (2)}~x^2-2xy+y^2+x-y-6$$

p.15 深める①$$\begin{split}&(x^2+x+1)(x^2-x+1)\\[2pt]~~=~&x^4-x^3+x^2+x^3-x^2+x+x^2-x+1\\[2pt]~~=~&x^4+x^2+1\end{split}$$
② \(x^2+1=A\) とおくと、$$\begin{split}&(A+x)(A-x)\\[2pt]~~=~&A^2-x^2\end{split}$$\(A=x^2+1\) と元に戻すと、$$\begin{split}~~=~&(x^2+1)^2-x^2\\[2pt]~~=~&x^4+2x^2+1-x^2\\[2pt]~~=~&x^4+x^2+1\end{split}$$

p.16 練習15$${\small (1)}~a^2+b^2+c^2+2ab-2bc-2ca$$$${\small (2)}~x^2+4y^2+9z^2+4xy+12yz+6zx$$

p.16 練習16$${\small (1)}~x^4-2x^2+1$$$${\small (2)}~x^4-1$$→ 式の展開の工夫

p.17 練習17$${\small (1)}~a(3b-2c)$$$${\small (2)}~4x^2(5x-2y^2)$$$${\small (3)}~ax(3a+6x+1)$$

p.17 練習18$${\small (1)}~(a+b)(c+d)$$$${\small (2)}~(x-2y)(a-b)$$

p.18 練習19$${\small (1)}~(x+5)^2$$$${\small (2)}~(x-6)^2$$$${\small (3)}~(x+3y)^2$$$${\small (4)}~(2a-b)^2$$$${\small (5)}~(x+3)(x-3)$$$${\small (6)}~(4a+5b)(4a-5b)$$

p.18 練習20$${\small (1)}~(x+2)(x+6)$$$${\small (2)}~(x-3)(x-4)$$$${\small (3)}~(x-2)(x+4)$$$${\small (4)}~(x+1)(x-6)$$$${\small (5)}~(a-4)(a-9)$$$${\small (6)}~(y+4)(y-5)$$$${\small (7)}~(x+y)(x+4y)$$$${\small (8)}~(x+9y)(x-2y)$$$${\small (9)}~(x+3a)(x-4a)$$→ ２次式の因数分解

p.19 深める\(-1\) と \(-8\) や \(-2\) と \(-4\) などでは、\(ad+bc\) の値が負となり、\(ad+bc=14\) とならないから

p.20 練習21$${\small (1)}~(x+2)(3x+1)$$$${\small (2)}~(x+2)(2x+5)$$$${\small (3)}~(x-2)(2x-3)$$$${\small (4)}~(2x+7)(2x-3)$$$${\small (5)}~(x-3)(6x+5)$$$${\small (6)}~(y-4)(2y-3)$$$${\small (7)}~(x+2a)(3x-a)$$$${\small (8)}~(3x+a)(2x-3a)$$$${\small (9)}~(x+5y)(4x-7y)$$→ 因数分解（たすき掛け）
→ 【問題演習】因数分解（たすき掛け）

p.20 練習22$${\small (1)}~(x-y-2)(x-y-3)$$$${\small (2)}~(x+y-1)(2x+2y+1)$$→ 因数分解の工夫

p.21 練習23$${\small (1)}~(x^2+1)(x+3)(x-3)$$$${\small (2)}~(x^2+4)(x+2)(x-2)$$→ 複２次式の因数分解

p.21 練習24$${\small (1)}~(x-1)(x+y-3)$$$${\small (2)}~(x-3)(x+3a+3)$$→ 文字式のたすき掛け
→ ２種類以上の文字を含む式の因数分解①（１次式）

p.22 練習25$${\small (1)}~(x+y-2)(x+y-3)$$$${\small (2)}~(x-y-2)(x-2y+3)$$$${\small (3)}~(x+y+3)(3x+y-2)$$$${\small (4)}~(2x+y+1)(x+2y-1)$$→ ２種類以上の文字を含む式の因数分解②（２次式）

p.22 深める\({\small (1)}~\)$$\begin{split}&2y^2+3(x-1)y+x^2-x-2\\[2pt]~~=~&2y^2+3(x-1)y+(x+1)(x-2)\\[2pt]~~=~&\{2y+(x+1)\}\{y+(x-2)\}\\[2pt]~~=~&(2y+x+1)(y+x-2)\end{split}$$\({\small (2)}~\)$$\begin{split}&3y^2+(5x+1)y+2x^2+2x-4\\[2pt]~~=~&3y^2+(5x+1)y+2(x+2)(x-1)\\[2pt]~~=~&\{3y+2(x+2)\}\{y+(x-1)\}\\[2pt]~~=~&(3y+2x+4)(y+x-1)\end{split}$$

p.23 研究 練習1$$~~~-(a-b)(b-c)(c-a)$$

p.24 発展 練習1$${\small (1)}~x^3+6x^2+12x+8$$$${\small (2)}~x^3-3x^2+3x-1$$$${\small (3)}~27a^3+27a^2b+9ab^2+b^3$$$${\small (4)}~x^3-6x^2y+12xy^2-8y^3$$

p.25 発展 練習2$${\small (1)}~x^3+8$$$${\small (2)}~x^3-27y^3$$→ ３次式の展開

p.25 発展 練習3$${\small (1)}~(x+3)(x^2-3x+9)$$$${\small (2)}~(x-1)(x^2+x+1)$$$${\small (3)}~(5x+a)(25x^2-5ax+a^2)$$→ ３次式の因数分解

p.27 練習26$${\small (1)}~0.\dot{8}$$$${\small (2)}~0.\dot{5}\dot{4}$$$${\small (3)}~0.\dot{3}7\dot{0}$$$${\small (4)}~1.1\dot{3}\dot{6}$$→ 循環小数と分数

p.30 練習27　自然数の乗法◯
　自然数の除法×
　　\(1\div2=0.5\) より自然数とならない
　整数の乗法◯
　整数の除法×
　　\(-1\div2=-0.5\) より整数とならない

p.30 練習28

p.31 練習29$${\small (1)}~3$$$${\small (2)}~4$$$${\small (3)}~{ \frac{\,2\,}{\,3\,}}$$$${\small (4)}~\sqrt{2}$$→ 絶対値の計算

p.31 練習30$$~~~5~,~-5$$

p.31 練習31$${\small (1)}~1$$$${\small (2)}~4$$$${\small (3)}~2-\sqrt{2}$$$${\small (4)}~\pi-3$$

p.32 練習32$${\small (1)}~\pm\sqrt{6}$$$${\small (2)}~4~,~-{ \frac{\,3\,}{\,5\,}}$$

p.33 練習33$${\small (1)}~\sqrt{6}$$$${\small (2)}~\sqrt{10}$$$${\small (3)}~\sqrt{2}$$$${\small (4)}~2$$

p.33 練習34$${\small (1)}~\sqrt{18}$$$${\small (2)}~\sqrt{48}$$$${\small (3)}~\sqrt{125}$$$${\small (4)}~\sqrt{{ \frac{\,3\,}{\,4\,}}}$$

p.33 練習35$${\small (1)}~2\sqrt{2}$$$${\small (2)}~2\sqrt{3}$$$${\small (3)}~5\sqrt{2}$$$${\small (4)}~3\sqrt{6}$$

p.34 練習36$${\small (1)}~4\sqrt{3}$$$${\small (2)}~-\sqrt{2}$$$${\small (3)}~3\sqrt{2}-4\sqrt{3}$$$${\small (4)}~5\sqrt{5}-\sqrt{6}$$

p.34 練習37$${\small (1)}~1+2\sqrt{10}$$$${\small (2)}~-12+15\sqrt{2}$$$${\small (3)}~10+2\sqrt{21}$$$${\small (4)}~10-4\sqrt{6}$$$${\small (5)}~1$$$${\small (6)}~4$$→ 平方根の計算

p.35 練習38$${\small (1)}~{ \frac{\,2\sqrt{3}\,}{\,3\,}}$$$${\small (2)}~2\sqrt{2}$$$${\small (3)}~{ \frac{\,\sqrt{6}\,}{\,2\,}}$$ $${\small (4)}~{ \frac{\,\sqrt{5}\,}{\,10\,}}$$

p.35 練習39$${\small (1)}~\sqrt{3}-\sqrt{2}$$$${\small (2)}~{ \frac{\,\sqrt{10}+\sqrt{6}\,}{\,2\,}}$$$${\small (3)}~{ \frac{\,\sqrt{15}-\sqrt{3}\,}{\,2\,}}$$$${\small (4)}~{ \frac{\,7+2\sqrt{10}\,}{\,3\,}}$$→ 分母の有理化

p.36 発展 練習1$${\small (1)}~\sqrt{5}+\sqrt{2}$$$${\small (2)}~3-\sqrt{3}$$$${\small (3)}~{ \frac{\,\sqrt{6}+\sqrt{2}\,}{\,2\,}}$$

p.38 練習40$${\small (1)}~x={ \frac{\,5\,}{\,3\,}}$$$${\small (2)}~x=-20$$$${\small (3)}~x=6$$

p.39 練習41$${\small (1)}~2x+3≧5$$$${\small (2)}~-2< a+b < 0$$$${\small (3)}~80x+100≦2000$$

p.41 練習42$${\small (1)}~<~,~<~,~>~,~>$$$${\small (2)}~<~,~<~,~>~,~>$$

p.41 練習43$${\small (1)}~<$$$${\small (2)}~<$$$${\small (3)}~<$$$${\small (4)}~>$$$${\small (5)}~<$$$${\small (6)}~>$$

p.43 練習44$${\small (1)}~x>2$$$${\small (2)}~x≦1$$$${\small (3)}~x>-3$$

p.44 練習45$${\small (1)}~x<2$$$${\small (2)}~x≦-5$$$${\small (3)}~x≧-3$$$${\small (4)}~x>{ \frac{\,5\,}{\,3\,}}$$

p.44 練習46$${\small (1)}~x≦7$$$${\small (2)}~x>{ \frac{\,18\,}{\,5\,}}$$→ １次不等式の解

p.45 練習47$${\small (1)}~-1≦x< 2$$$${\small (2)}~x< -{ \frac{\,3\,}{\,5\,}}$$

p.46 練習48$${\small (1)}~1≦x≦5$$$${\small (2)}~-1 < x< { \frac{\,4\,}{\,3\,}}$$→ 連立不等式の解

p.46 深める\({\small (2)}~\)$$~~~\begin{eqnarray} \left\{\begin{array}{l}
-1≦2x-3 ~&\cdots{\large ①}\\
2x-3≦8 ~&\cdots{\large ②}
\end{array}\right.\end{eqnarray}$$①より、$$\begin{eqnarray}~~~-1&≦&2x-3\\[2pt]~~~-2x&≦&-2\\[2pt]~~~x&≧&1\end{eqnarray}$$②より、$$\begin{eqnarray}~~~2x-3&≦&8\\[2pt]~~~2x&≦&11\\[3pt]~~~x&≦&\frac{\,11\,}{\,2\,}\end{eqnarray}$$①と②の共通範囲を求めて、$$~~~1≦x≦\frac{\,11\,}{\,2\,}$$

p.47 練習49$$~~~15$$

p.47 練習50$$~~~10$$→ 不等式を満たす整数の解

p.47 練習51　\(12\) 個
→ 不等式の文章問題

p.48 練習52$${\small (1)}~x=\pm2$$$${\small (2)}~-2< x < 2$$$${\small (3)}~x< -4~,~4< x$$$${\small (3)}~-4≦x≦4$$

p.49 練習53$${\small (1)}~x=-2~,~-6$$$${\small (2)}~-2< x < 8$$$${\small (3)}~x≦1~,~3≦x$$→ 絶対値を含む方程式と不等式

p.49 研究 練習1\({\small (1)}~\)
\(~~~x≧3\) のとき、\(|x-3|=x-3\)
\(~~~x<3\) のとき、\(|x-3|=-x+3\)
\({\small (2)}~\)
\(~~~x≧-2\) のとき、\(|x+2|=x+2\)
\(~~~x<-2\) のとき、\(|x+2|=-x-2\)

p.50 研究 練習2$${\small (1)}~x=1$$$${\small (2)}~x≧1$$$${\small (3)}~x< { \frac{\,1\,}{\,4\,}}$$