13.1.5: Chapter 5

Be Prepared

5.1

$11x^2+8x+6$

5.2

$3n+9$

5.3

$-200$

5.4

$-8$

5.5

$\frac{x}{3y}$

5.6

$-10.946$

5.7

$2x+6$

5.8

ⓐ $81$; ⓑ $81$; ⓒ $-81$

5.9

$21$

5.10

$\frac{3+x}{d}$

5.11

$6y^2$

5.12

$11a^2+7a+5$

Try It

5.1

ⓐ monomial, 0
ⓑ polynomial, 3 ⓒ trinomial, 4
ⓓ binomial, 2 ⓔ monomial, 10

5.2

ⓐbinomial, 3 ⓑ trinomial, 3 ⓒ monomial, 0 ⓓ polynomial, 4 ⓔ monomial, 7

5.3

ⓐ $21q^2$ ⓑ $13m{n}^3$

5.4

ⓐ $\mathrm{-7}{c}^2$ ⓑ $\mathrm{-10}{y}^2{z}^3$

5.5

ⓐ $5y^2+3z^2$
ⓑ $m^2{n}^2-8m^2+4n^2$

5.6

ⓐ $\mathrm{-4}{m}^2+n^2$
ⓑ $p{q}^2-6p-5q^2$

5.7

$8x^2-11x+8$

5.8

$17y^2+14y+1$

5.9

$x^2+3x-5$

5.10

$6b^2+3$

5.11

$\mathrm{-5}ab+7b^2$

5.12

$7mn+4n^2$

5.13

$5x^2-5xy+5y^2$

5.14

$7x^2-6xy-2y^2$

5.15

$x^3-y^3$

5.16

$p^3-3p^{2}q+q^3$

5.17

ⓐ 18 ⓑ 50 ⓒ $\mathrm{-15}$

5.18

ⓐ 20 ⓑ 2 ⓒ $\mathrm{-4}$

5.19

The height is $150$ feet.

5.20

The height is 31 feet.

5.21

ⓐ $(f+g)(x)=3x^2-6x-3$ ⓑ $(f+g)(3)=6$
ⓒ $(f-g)(x)=x^2-2x+9$
ⓓ $(f-g)(\mathrm{-2})=17$

5.22

ⓐ $(f+g)(x)=6x^2-x+7$ ⓑ $(f+g)(3)=58$
ⓒ $(f-g)(x)=4x^2-7x-9$
ⓓ $(f-g)(\mathrm{-2})=21$

5.23

ⓐ $b^{17}$ ⓑ $4^{3x}$ ⓒ $12p^6$
ⓓ $x^{18}$

5.24

ⓐ $x^{16}$ ⓑ ${10}^{x+1}$ ⓐ $12z^8$
ⓓ $b^{19}$

5.25

ⓐ $x^5$ ⓑ $6^9$ ⓒ $\frac{1}{x^4}$
ⓓ $\frac{1}{{12}^{15}}$

5.26

ⓐ $y^6$ ⓑ ${10}^8$ ⓒ $\frac{1}{m^8}$
ⓓ $\frac{1}{9^{11}}$

5.27

ⓐ 1 ⓑ 1

5.28

ⓐ 1 ⓑ 1

5.29

ⓐ $\frac{1}{z^3}$ ⓑ $\frac{1}{{10}^7}$ ⓒ $p^8$ ⓓ $64$

5.30

ⓐ $\frac{1}{n^2}$ ⓑ $\frac{1}{\mathrm{10,000}}$ ⓒ $q^7$
ⓓ $16$

5.31

ⓐ $\frac{81}{16}$ ⓑ $\frac{n^2}{m^2}$

5.32

ⓐ $\frac{125}{27}$ ⓑ $\frac{b^4}{a^4}$

5.33

ⓐ $\frac{1}{z^9}$ ⓑ $\frac{1}{p^3{q}^3}$ ⓒ $-\frac{12v^5}{u}$

5.34

ⓐ $\frac{1}{c^{15}}$ ⓑ $\frac{1}{r^2{s}^8}$ ⓒ $\frac{30d^3}{c^8}$

5.35

ⓐ $b^{35}$ ⓑ $5^{12}$ ⓒ $a^{48}$

5.36

ⓐ $z^{54}$ ⓑ $3^{49}$ ⓒ $q^{29}$

5.37

ⓐ $32w^5{x}^5$ ⓑ 1 ⓒ $\frac{1}{16b^{12}}$
ⓓ $\frac{64}{a^8}$

5.38

ⓐ $\mathrm{-27}{y}^3$ ⓑ 1 ⓒ $\frac{1}{16x^8}$
ⓓ $\frac{8}{c^{12}}$

5.39

ⓐ $\frac{p^4}{10000}$ ⓑ $\frac{n^7}{m^7}$
ⓒ $\frac{81a^4{b}^{12}}{c^8}$ ⓓ $\frac{27}{x^6{y}^9}$

5.40

ⓐ $\frac{\mathrm{-8}}{q^3}$ ⓑ $\frac{x^4}{w^4}$ ⓒ $\frac{x^2{y}^6}{9z^4}$
ⓓ $\frac{8n^6}{m^6}$

5.41

ⓐ $81c^{24}{d}^{30}$ ⓑ $\frac{1}{a^{18}}$
ⓒ $y^{15}$

5.42

ⓐ $256a^{22}{b}^{24}$ ⓑ $\frac{1}{p^{39}}$
ⓒ $2x^3{y}^{10}$

5.43

ⓐ $9.6\times {10}^4$ ⓑ $7.8\times {10}^{\mathrm{-3}}$

5.44

ⓐ $4.83\times {10}^4$
ⓑ $1.29\times {10}^{\mathrm{-2}}$

5.45

ⓐ 1,300 ⓑ $\mathrm{-0.00012}$

5.46

ⓐ $\mathrm{-950,000}$ ⓑ 0.075

5.47

ⓐ $\mathrm{-0.006}$ ⓑ 20,000

5.48

ⓐ $\mathrm{-0.009}$ ⓑ 400,000

5.49

ⓐ $\mathrm{-35}{y}^{11}$ ⓑ $6a^5{b}^6$

5.50

ⓐ $54b^9$ ⓑ $8r^{11}{s}^8$

5.51

ⓐ$\mathrm{-15}{y}^3-24y^2+21y$
ⓑ $12x^4{y}^2-20x^3{y}^3+12x^2{y}^4$

5.52

ⓐ $8x^4-24x^3+20x^2$
ⓑ $\mathrm{-18}{a}^{5}b+12a^4{b}^2-36a^3{b}^3$

5.53

ⓐ$x^2+17x+72$
ⓑ $15c^2+14c-8$

5.54

ⓐ $20x^2+51x+27$
ⓑ $30y^2-3y-6$

5.55

ⓐ $x^2-2x-35$
ⓑ $15x^2+29x-14$

5.56

ⓐ $b^2+3b-18$
ⓑ $16y^2-20y-50$

5.57

ⓐ$x^3-8x^2+6x-48$
ⓑ $8a^2{b}^2+12ab-20$

5.58

ⓐ$y^3-9y^2+7y-63$
ⓑ $8x^2{y}^2+2xy-15$

5.59

$15m^2-51m+42$

5.60

$42b^2-53b+15$

5.61

ⓐ $y^3-8y^2+17y-6$
ⓑ $y^3-8y^2+17y-6$

5.62

ⓐ $2x^3+5x^2-7x+20$
ⓑ $y^3-8y^2+17y-6$

5.63

ⓐ$x^2+18x+81$
ⓑ $4c^2-4cd+d^2$

5.64

ⓐ$y^2+22y+121$
ⓑ $16x^2-40xy+25y^2$

5.65

ⓐ $36x^2-25$
ⓑ$16p^2-49q^2$

5.66

ⓐ $4x^2-49$ ⓑ $9x^2-y^2$

5.67

ⓐ FOIL; $18b^2+77b-18$
ⓑ Binomial Squares; $81p^2-72p+16$
ⓒ Binomial Squares; $49y^2+14y+1$
ⓓ Product of Conjugates; $16r^2-9$

5.68

ⓐ Binomial Squares; $36x^2+84x+49$ ⓑ Product of Conjugates; $9x^2-16$ ⓒ FOIL; $10x^2-29x+10$ ⓓ Binomial Squares; $36n^2-12n+1$

5.69

ⓐ $\left(f·g\right)\left(x\right)=x^3-7x^2+13x-15$
ⓑ $\left(f·g\right)\left(2\right)=\mathrm{-9}$

5.70

ⓐ $\left(f·g\right)\left(x\right)=x^3+x^2-52x-28$
ⓑ $\left(f·g\right)\left(2\right)=\mathrm{-120}$

5.71

$-\frac{9}{a^{5}b}$

5.72

$\frac{\mathrm{-9}d}{c^4}$

5.73

$\frac{4y^2}{7x^4}$

5.74

$\frac{5}{8m^5{n}^3}$

5.75

$\mathrm{-4}a+2b$

5.76

$8a^{5}b+6a^3{b}^2$

5.77

$y+7$

5.78

$m+5$

5.79

$x^3-3x^2+2x+1+\frac{3}{x+3}$

5.80

$x^3-3x^2-2x-1-\frac{3}{x+3}$

5.81

$x^2+4x+16$

5.82

$25x^2+10x+4$

5.83

$3x^2+4x-2\text{;}2$

5.84

$4x^2-3x+1\text{;}1$

5.85

$x^3-4x^2+5\text{;}0$

5.86

$x^3-3x^2+2\text{;}0$

5.87

ⓐ $\left(\frac{f}{g}\right)\left(x\right)=x-8$
ⓑ $\left(\frac{f}{g}\right)\left(\mathrm{-3}\right)=\mathrm{-11}$

5.88

ⓐ $\left(\frac{f}{g}\right)\left(x\right)=x-9$
ⓑ undefined

5.89

$\mathrm{-1}$

5.90

$6$

5.91

yes

5.92

yes

Section 5.1 Exercises

1.

ⓐ trinomial, 5 ⓑ polynomial, 3 ⓒ binomial, 2 ⓓ monomial, 0
ⓔ binomial, 2

3.

ⓐ binomial, 1ⓑ trinomial, 2
ⓒ polynomial, 3ⓓ trinomial, 5
ⓔ monomial, 0

5.

ⓐ $\text{trinomial,}2$ ⓑ $\text{monomial,}4$ ⓒ $\text{binomial,}1$ ⓓ $\text{polynomial,}3$
ⓔ $\text{monomial,}0$

7.

ⓐ $\text{binomial,}1$ ⓑ $\text{trinomial,}2$ ⓒ $\text{polynomial,}3$ ⓓ $\text{binomial,}3$
ⓔ $\text{monomial,}0$

9.

ⓐ ${\text{12x}}^{\text{2}}$ ⓑ $\text{−}\text{5a}$

11.

ⓐ $\text{6}w$ ⓑ $19x^{2}y$

13.

${\text{12x}}^{\text{2}}-\text{5a}$

15.

$6w+19x^{2}y$

17.

ⓐ $\mathrm{-22}b$ ⓑ $16xy$

19.

ⓐ $\mathrm{-10}a+5b$
ⓑ $p{q}^2-4p-3q^2$

21.

ⓐ $\mathrm{-4}{a}^2+b^2$
ⓑ $x^{2}y-3x+7x{y}^2$

23.

ⓐ $x{y}^2-5x-5y^2$
ⓑ $19y+5z$

25.

$x-3y+a^{2}b-4a-5a{b}^2$

27.

$\text{−}{u}^2+4v^2+\text{12a}+8b$

29.

$\text{−}\text{4a}-3b$

31.

$\mathrm{-17}{x}^6$

33.

$11y^2+4y+11$

35.

$\mathrm{-3}{x}^2+17x-1$

37.

$11x^2-5x+5$

39.

$6a^2-4a-1$

41.

$2m^2-7m+4$

43.

$11a+3$

45.

$12s^2-16s+9$

47.

$3x^2-x+4$

49.

$w^2+3w+4$

51.

$11w-66$

53.

$10x^2-7xy+6y^2$

55.

$10m^2+3mn-8n^2$

57.

$\mathrm{-3}ab+3b^2$

59.

$p^3-6p^{2}q+p{q}^2+4q^3$

61.

$x^3+2x^{2}y-5x{y}^2+y^3$

63.

ⓐ 187 ⓑ 40 ⓒ 2

65.

ⓐ $\mathrm{-104}$ ⓑ 4 ⓒ 40

67.

The height is 11 feet.

69.

The revenue is $10,800.

71.

The cost is $456.

73.

ⓐ $(f+g)(x)=7x^2+4x+4$ ⓑ $(f+g)(2)=40$
ⓒ $(f-g)(x)=\mathrm{-3}{x}^2-12x-2$
ⓓ $(f-g)(\mathrm{-3})=7$

75.

ⓐ $(f+g)(x)=6x^3-x^2-9x+3$
ⓑ $(f+g)(2)=29$
ⓒ $(f-g)(x)=\text{−}{x}^2+5x+3$
ⓓ $(f-g)(\mathrm{-3})=\mathrm{-21}$

77.

Answers will vary.

79.

Answers will vary.

Section 5.2 Exercises

81.

ⓐ $d^9$ ⓑ $4^{14x}$ ⓒ $8y^4$ ⓓ $w^6$

83.

ⓐ $n^{31}$ ⓑ $3^{x+6}$ ⓒ $56w^6$
ⓓ $a^{16}$

85.

$m^{x+3}$

87.

$y^{a+b}$

89.

ⓐ $x^{15}$ ⓑ $5^9$ ⓒ $\frac{1}{q^{18}}$ ⓓ $\frac{1}{10}$

91.

ⓐ $p^{14}$ ⓑ $4^{12}$ ⓒ $\frac{1}{b^8}$ ⓓ $\frac{1}{4^5}$

93.

ⓐ 1 ⓑ 1

95.

ⓐ $\mathrm{-1}$ ⓑ $\mathrm{-1}$

97.

ⓐ $\frac{1}{a^2}$ ⓑ $\frac{1}{1000}$ ⓒ $c^5$ ⓓ $9$

99.

ⓐ $\frac{1}{r^3}$ ⓑ $\frac{1}{\mathrm{100,000}}$ ⓒ $q^{10}$
ⓓ $\mathrm{1,000}$

101.

ⓐ $\frac{64}{25}$ ⓑ $\frac{a^2}{b^2}$

103.

ⓐ $\frac{729}{64}$ ⓑ $-\frac{v^5}{u^5}$

105.

ⓐ $\frac{1}{25}$ ⓑ $-\frac{1}{25}$ ⓒ $25$ ⓓ $\mathrm{-25}$

107.

ⓐ $\frac{3}{5}$ ⓑ $\frac{1}{15}$

109.

ⓐ $\frac{1}{b^4}$ ⓑ $\frac{w^2}{x^9}$ ⓒ $\mathrm{-12}c{d}^4$

111.

ⓐ 1 ⓑ $\frac{1}{u^4{v}^5}$ ⓒ $\frac{-36r^2}{s^5}$

113.

$\frac{1}{p}$

115.

ⓐ $m^8$ ⓑ ${10}^{18}$ ⓒ $\frac{1}{x^{12}}$

117.

ⓐ $y^{3x}$ ⓑ $5^{xy}$ ⓒ $\frac{1}{q^{48}}$

119.

ⓐ $9x^2{y}^2$ ⓑ 1 ⓒ $\frac{1}{25x^4}$
ⓓ $\frac{16}{y^6}$

121.

ⓐ $\mathrm{-125}{a}^3{b}^3$ ⓑ 1 ⓒ $\frac{1}{36x^6}$ ⓓ $\frac{9}{y^8}$

123.

ⓐ $\frac{p^5}{32}$ ⓑ $\frac{y^6}{x^6}$ ⓒ $\frac{8x^3{y}^6}{z^3}$
ⓓ $\frac{16}{p^6{q}^4}$

125.

ⓐ $\frac{a^4}{81b^4}$ ⓑ $\frac{16m^2}{25}$ ⓒ $\frac{a^4{c}^4}{9b^6}$ ⓓ $\frac{q^8{r}^8}{p^2}$

127.

ⓐ $1125t^8$ ⓑ $\frac{1}{t^{19}}$ ⓒ $\frac{y^4}{3x^2}$

129.

ⓐ $16m^8{n}^{22}$ ⓑ $\frac{4}{p^6}$

131.

ⓐ $\frac{7}{n}$ ⓑ $\frac{1}{7n}$ ⓒ $-\frac{1}{7n}$

133.

ⓐ $\frac{1}{9p^2}$ ⓑ $\frac{3}{p^2}$ ⓒ $\frac{\mathrm{-3}}{p^2}$

135.

$x^{14}$

137.

$a^{36}$

139.

$8m^{18}$

141.

$\mathrm{1,000}{x}^6{y}^3$

143.

$16a^{12}{b}^8$

145.

$\frac{8}{27}{x}^6{y}^3$

147.

$\mathrm{1,024}{a}^{10}$

149.

$\mathrm{25,000}{p}^{24}$

151.

$x^{18}{y}^{18}$

153.

$144m^8{n}^{22}$

155.

ⓐ $45x^3$ ⓑ $48y^4$

157.

ⓐ $\frac{1}{2r^4}$ ⓑ $\frac{1}{3}{x}^{11}$

159.

$\frac{1}{j^3}$

161.

$-\frac{4000}{n^{12}}$

163.

ⓐ $3.4\times {10}^5$ ⓑ $4.1\times {10}^{\mathrm{-2}}$

165.

ⓐ $1.29\times {10}^6$
ⓑ $1.03\times {10}^{\mathrm{-6}}$

167.

ⓐ $\mathrm{-830}$ ⓑ 0.038

169.

ⓐ 16,000,000,000
ⓑ 0.00000843

171.

ⓐ 0.02 ⓑ 500,000,000

173.

ⓐ 0.0000056 ⓑ 20,000,000

175.

Answers will vary.

177.

Answers will vary.

Section 5.3 Exercises

179.

ⓐ$30x^8$ ⓑ $15x^8{y}^2$

181.

ⓐ $72c^5$ ⓑ $\frac{1}{3}{m}^5{n}^5$

183.

ⓐ $\mathrm{-5}{t}^3-15t^2+90t$
ⓑ $9s{r}^5-27s^2{r}^4+45s^3{r}^3$

185.

ⓐ $\mathrm{-5}{m}^3-15m^2+90m$
ⓑ $\mathrm{-21}{x}^4{y}^2-30x^3{y}^3+3x^2{y}^4$

187.

$y^2+12y+27$

189.

$21q^2-44q-32$

191.

$y^2-8y+12$

193.

$6p^2+11p+5$

195.

$m^2+7m-44$

197.

$33r^2-85r-8$

199.

$y^3+3y^2-4y-12$

201.

$6x^2{y}^2+13xy+6$

203.

$y^4-11y^2+28$

205.

$9r^2{s}^2-33rs+28$

207.

$u^3+7u^2+14u+8$

209.

$3a^3+31a^2+5a-50$

211.

$6a^4-13a^3+15a^2+35a-50$

213.

$p^3-10p^2+33p-36$

215.

$6r^3-41r^2-61r-9$

217.

$q^2+24q+144$

219.

$4y^2-12yz+9z^2$

221.

$x^2+\frac{4}{3}x+\frac{4}{9}$

223.

$\frac{1}{64}{x}^2-\frac{1}{36}xy+\frac{1}{81}{y}^2$

225.

$25u^4+90u^2+81$

227.

$64p^6-48p^3+9$

229.

$64j^2-16$

231.

$81c^2-25$

233.

$49w^2-100x^2$

235.

$p^2-\frac{16}{25}{q}^2$

237.

$x^2{y}^2-81$

239.

$225m^4-64n^8$

241.

$t^2-18t+81$

243.

$2x^2-3xy-2y^2$

245.

$9p^2-64$

247.

$k^2-12k+36$

249.

$8x^3-x^2{y}^2+64xy-8y^3$

251.

$y^8+4y^{4}z+4z^2$

253.

$m^6-16m^{3}n+64n^2$

255.

$r^5+r^2{s}^2-r^3{s}^3-s^5$

257.

$18p-9$

259.

$\mathrm{-10}j-15$

261.

$9d^7$

263.

$42m^5{n}^8$

265.

$5q^5-10q^4+30q^3$

267.

$y^3-y^2-2y$

269.

$6k^3+11k^2-26k+4$

271.

$121-b^2$

273.

$4x^4-9y^8$

275.

$9d^2+6d+1$

277.

$9z^2+\frac{6}{5}z+\frac{1}{25}$

279.

ⓐ $\left(f·g\right)\left(x\right)=4x^3-x^2-8x+5$
ⓑ $\left(f·g\right)\left(\mathrm{-2}\right)=\mathrm{-15}$

281.

ⓐ $\left(f·g\right)\left(x\right)=49x^2-64$
ⓑ $\left(f·g\right)\left(\mathrm{-2}\right)=132$

283.

ⓐ $\left(f·g\right)\left(x\right)=x^4+6x^3+9x^2+10x-12$ ⓑ $\left(f·g\right)\left(1\right)=14$

285.

Answers will vary.

287.

Answers will vary.

Section 5.4 Exercises

289.

$\frac{2m^3}{3n^5}$

291.

$\frac{\mathrm{-3}{y}^3}{4x^3}$

293.

$\frac{\mathrm{-3}{q}^5}{p^5}$

295.

$\frac{5v^4}{u^2}$

297.

$4x^2+3x$

299.

$\mathrm{-6}{y}^2+3y$

301.

$6r^3+11r^{2}s-8r{s}^3$

303.

$\mathrm{-5}y-3+\frac{1}{4y}$

305.

$a-7$

307.

$4x+3$

309.

$p+3-\frac{8}{p+8}$

311.

$2n^2-6n+8+\frac{4}{n+3}$

313.

$m^2-10m+100$

315.

$25y^2+20y+16$

317.

$x^2-5x+6\text{;}0$

319.

$2x^2-3x+4\text{;}4$

321.

$x^3-2x^2+5x-4\text{;}\text{−}2$

323.

$3x^3-2x^2-4x-2\text{;}0$

325.

ⓐ $\left(\frac{f}{g}\right)\left(x\right)=x-6$
ⓑ $\left(\frac{f}{g}\right)\left(\mathrm{-5}\right)=\mathrm{-11}$

327.

ⓐ $\left(\frac{f}{g}\right)\left(x\right)=x^2+5x-4$
ⓑ $\left(\frac{f}{g}\right)\left(0\right)=\mathrm{-4}$

329.

ⓐ $\left(f·g\right)\left(x\right)=x^4+6x^3+9x^2+10x-12;$ ⓑ $\left(f·g\right)\left(1\right)=14$

331.

$\mathrm{-9}$

333.

−6

335.

no

337.

yes

339.

answer will vary

341.

Answers will vary.

Review Exercises

343.

binomial

345.

trinomial

347.

$\mathrm{-13}{y}^3$

349.

$6m^2+19m-4$

351.

$5u^2+4u+7$

353.

$14x-7$

355.

$\mathrm{-7}b-3a$

357.

$8a^2-5a-2$

359.

$3m^2-3m+3$

361.

$3y^2-8y-14$

363.

$x^3+2x^{2}y-5x{y}^2+y^3$

365.

ⓐ 165 ⓑ 39 ⓒ 5

367.

The height is $64\text{feet}$.

369.

ⓐ $(f+g)(x)=4x^2-5x-2$ ⓑ $(f+g)(3)=19$
ⓒ $(f-g)(x)=\mathrm{-3}x-12$
ⓓ $(f-g)(\mathrm{-2})=\mathrm{-6}$

371.

$p^{13}$

373.

$a^6$

375.

$y^{a+b}$

377.

$a^5$

379.

$\frac{1}{x^5}$

381.

1

383.

$\mathrm{-3}$

385.

$-\frac{1}{1000}$

387.

$\frac{1}{8n}$

389.

$\frac{1}{1000}$

391.

36

393.

$\mathrm{-125}$

395.

$-\frac{1}{125}$

397.

$\frac{{-x}^3}{27}$

399.

$3^{10}$

401.

$x^6$

403.

$\frac{1}{u^3{v}^5}$

405.

$\frac{1}{p}$

407.

$\frac{1}{q^{16}}$

409.

$n^2$

411.

1

413.

$\frac{9}{y^8}$

415.

$\frac{81x^4{y}^8}{z^4}$

417.

$27x^7{y}^{17}$

419.

$\frac{3y^4}{4x^4}$

421.

$5.3\times {10}^6$

423.

$\mathrm{29,000}$

425.

$0.00009413$

427.

$0.00072$

429.

$\mathrm{9,000}$

431.

$10c^{10}$

433.

$\frac{m^7{n}^{10}}{9}$

435.

$a^4-9a^3-36a^2$

437.

$8n^4-10n^3$

439.

$y^2+8y-48$

441.

$18p^2-93p+110$

443.

$k^2-3k-54$

445.

$10y^2-59y+63$

447.

$x^2+x-72$

449.

$30a^2-33a+3$

451.

$15b^3-b^2-47b+18$

453.

$24y^3-54y^2+32y-5$

455.

$x^2+\frac{3}{2}x+\frac{9}{16}$

457.

$25p^2+70pq+49q^2$

459.

$36x^2-y^2$

461.

$144x^6-49y^4$

463.

$9p^9$

465.

$-\frac{3}{y^4}$

467.

$\frac{4a^5}{b^2}$

469.

$\frac{4m^9}{n^4}$

471.

$\mathrm{-9}{y}^2+4y$

473.

$\mathrm{-3}x-1+\frac{3}{4x}$

475.

$y-3+\frac{33}{y+5}$

477.

$a^2-a+1-\frac{2}{a+1}$

479.

$2x^2-5x-4\text{;}0$

481.

ⓐ $\left(\frac{f}{g}\right)\left(x\right)=x-6$
ⓑ $\left(\frac{f}{g}\right)\left(\mathrm{-2}\right)=\mathrm{-8}$

483.

$\mathrm{-9}$

485.

no

Practice Test

487.

ⓐ trinomial ⓑ 4

489.

$6x^2-3x+11$

491.

$x$

493.

$1$

495.

$\frac{1}{8y^3}$

497.

$x^9$

499.

$\frac{4r}{s^6}$

501.

$\mathrm{-48}{x}^5{y}^9$

503.

$7m^2+19m-6$

505.

$16x^2-24x+9$

507.

$3y^2-7x$

509.

yes

511.

$4.8\times {10}^3$

513.

ⓐ $36$ ⓑ $21$ ⓒ $-9$

515.

ⓐ $\left(\frac{f}{g}\right)\left(x\right)=3x+4$
ⓑ $\left(\frac{f}{g}\right)\left(3\right)=13$