25 $(x - 2)^2 - 4(x - 2) - 2$

26 (a) irreducible (b) 不是不可约的
(c) 不是不可约的 (d) irreducible

27 (a) 在……处取极小值 $x = -1$ of 2
(b) 最小值在 $x = \frac{3}{2}$ of 0
(c) 在……处取得最大值 $x = -\frac{2}{3}$ of $\frac{22}{3}$
(d) 在……处取得最大值 $x = \frac{3}{10}$ of $-\frac{11}{20}$

28 (a) $x < 2$ and $x > 4$
(b) $-\frac{5}{2} < x < 3$

29 315 feet, 46 mph

30 (a) $(x - 1)(x + 3)(x - 4)$
(b) $(x + 1)(x - 2)(x + 3)$
(c) $(x - 1)(x + 1)(x^2 + 2)$
(d) $x(x - 1)(2x + 3)(x + 2)$
(e) $(x - 1)^2(2x - 1)(x - 2)$
(f) $(x^2 + 9)(x - 2)(x + 2)$

31 2, 7, 139, 527, 524

32 $y = (x - 5)^4 + 15(x - 5)^3 + 80(x - 5)^2 + 165(x - 5) + 81$ . 由于系数全为正, 的零点 $y$ 必须都位于……的左侧 $x = 5$ , 也就是说 $x < 5$ . 因此，的零点 $y$ 介于……之间 $x = 0$ and $x = 5$ .

33 (a) $x^2 - 14x + 1 = 0$
(b) $x^2 + 52x + 1 = 0$

34 $x^3 - 5x^2 + 1$

35 $3x^2 + 22x + 378$

36 (b) $r = 10/(4\pi)^{1/3}$ , $h = 20/(4\pi)^{1/3}$

37 $0.096 \text{ m}^3$ , $0.1875 \text{ m}^3$

38 $x_0 = 10.94$ , 巷道宽度 = $4.92 \text{ m}$

39 (a) $1 + (x + 2)/[(x + 1)(x - 1)]$
(b) $x^3 - 2x^2 + x + 1 - 3x/(x^2 + x + 1)$

40 (a) $(-5x^2 + x - 2)/[x(x - 2)(x^2 + 1)]$
(b) $2/[(x - 1)^3(x + 1)]$
(c) $(4x^4 - 11x^3 + 10x^2 - 5x + 4)/[(x^2 + 1)(x - 1)^2(x - 2)]$

41 (a) $\frac{\frac{1}{3}}{x - 2} - \frac{\frac{1}{3}}{x + 1}$
(b) $\frac{1}{x - 2} + \frac{1}{x + 1}$
(c) $1 + \frac{\frac{2}{3}}{x - 2} + \frac{\frac{1}{3}}{x + 1}$
(d) $\frac{\frac{1}{3}}{(x - 2)^2} + \frac{\frac{2}{9}}{x - 2} - \frac{\frac{2}{9}}{x + 1}$
(e) $\frac{1}{x + 1} - \frac{x + 1}{x^2 + 2x + 2}$
(f) $\frac{-\frac{1}{3}}{x + 1} + \frac{\frac{1}{12}}{x - 2} + \frac{\frac{1}{4}}{x + 2}$

42 (a) $\frac{\frac{1}{3}}{x - 4} - \frac{\frac{1}{3}}{x - 1}$
(b) $\frac{\frac{1}{3}}{x - 1} - \frac{\frac{1}{3}x + \frac{2}{3}}{x^2 + x + 1}$
(c) $\frac{\frac{5}{9}}{x - 2} + \frac{\frac{4}{3}}{(x + 1)^2} - \frac{\frac{5}{9}}{x + 1}$
(d) $1 - \frac{3}{x - 2} + \frac{8}{x - 3}$
(e) $\frac{1}{x^2 + 1} + \frac{x - 2}{(x^2 + 1)^2}$
(f) $\frac{x + 1}{x^2 + 4} + \frac{2}{x - 1} - \frac{3}{x + 5}$

43 (a) $(\sqrt[2]{2}, \sqrt[2]{2})$ , $(-\sqrt[2]{2}, -\sqrt[2]{2})$
(b) $(\sqrt[2]{2}, \sqrt[2]{2})$ , $(-\sqrt[2]{2}, -\sqrt[2]{2})$
(c) $(-\sqrt[2]{5}, -\sqrt[2]{5})$ , $(\sqrt[2]{5}, \sqrt[2]{5})$ , $(\sqrt[2]{2}, \sqrt[2]{2})$ , $(-\sqrt[2]{2}, -\sqrt[2]{2})$
(d) 在定义域上不相交

44 (a) asymptotes: $y = x - 8$ , $x = 0$ ,
maximum $(\sqrt{15}, -8 + 2\sqrt{15})$ ,
minimum $(-\sqrt{15}, -8 - 2\sqrt{15})$
(b) asymptotes: $y = 1$ , $x = 1$ (c) $y = x$ , $x = -5$

45 $y = -1 \pm \sqrt{(x + 4)}$ , $(y + 1)^2 = x + 4$

48 $0.6, 0.8, 0.75, 36.87^\circ = 36^\circ 52' 12''$ ;
$\frac{12}{13}, \frac{5}{13}, 2.4, 67.38^\circ = 67^\circ 22' 48''$

49 AB = 29.44, BC = 33.04 m

50 30

51 60

52 AB = 30.6 mm, AC = 26.9 mm

53 45.5 mm

55 degrees $0^\circ$ $30^\circ$ $45^\circ$ $60^\circ$ $90^\circ$ $120^\circ$ $150^\circ$ $180^\circ$
radians $0$ $\frac{1}{6}\pi$ $\frac{1}{4}\pi$ $\frac{1}{3}\pi$ $\frac{1}{2}\pi$ $\frac{2}{3}\pi$ $\frac{5}{6}\pi$ $\pi$
degrees $210^\circ$ $225^\circ$ $240^\circ$ $270^\circ$ $300^\circ$ $315^\circ$ $330^\circ$ $360^\circ$
radians $\frac{7}{6}\pi$ $\frac{5}{4}\pi$ $\frac{4}{3}\pi$ $\frac{3}{2}\pi$ $\frac{5}{3}\pi$ $\frac{7}{4}\pi$ $\frac{11}{6}\pi$ $2\pi$

57 (a) $0.3398, 2.8018, \frac{3}{2}\pi$
(b) $1.8235, 4.4597, \pi$
(c) $2.6779, 5.8195, \frac{1}{4}\pi, \frac{5}{4}\pi$
(d) $\frac{1}{2}\pi, \frac{3}{2}\pi, \frac{1}{6}\pi, \frac{5}{6}\pi$

58 $\frac{1}{2}\sqrt{3}, \sqrt{3}, \frac{1}{2}\sqrt{3}, \frac{1}{2}$
$\frac{1}{2}\sqrt{(2 - \sqrt{3})}, \frac{1}{2}\sqrt{(2 + \sqrt{3})}, 2 - \sqrt{3}$
(a) $\frac{1}{2}\sqrt{3}$ (b) $1/\sqrt{3}$
(c) $\frac{1}{2}\sqrt{3}$ (d) $\frac{1}{2}\sqrt{(2 + \sqrt{3})}$
(e) $-\frac{1}{2}\sqrt{(2 - \sqrt{3})}$ (f) $-(2 - \sqrt{3})$

59 (a) $-\sqrt{(1 - s^2)}$ (b) $-2s\sqrt{(1 - s^2)}$
(c) $s(3 - 4s^2)$ (d) $\sqrt{{\frac{1}{2}[1 + \sqrt{(1 - s^2)}]}}$

61 $x = n\pi$ ( $n = \pm 1, \pm 3, \dots$ )
and $x = 0.9273 + 2n\pi$ ( $n = 0, \pm 1, \pm 2, \dots$ )