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Intermediate Algebra (11th edition)

(Marvins-Underground-K-12) #1

Section 6.2 (pages 332–333)


1.D 3.B 5. 7. 9.prime





    1. 15.prime




















27.prime 29. 31.

















    1. 45.She did not factor




the polynomial completely. The factor can be factored
further into giving the final form as








































Section 6.3 (pages 337–339)


1.A, D 3.B, C 5.The sum of two squares can be factored


if the binomial terms have a common factor greater than 1.
































































































  19. 69.The product must equal
    Multiply to verify this.




70.Start by factoring as a difference of squares.
71.










  4. 12 x+y 21 a-b 2 81. 1 p+ 721 p- 32




18 m- 9 n 218 m+ 9 n- 64 m^2 - 72 mn- 81 n 22

1 t- 3212 t+ 1214 t 2 - 2 t+ 12

13 a- 4 b 219 a^2 + 12 ab+ 16 b^2 + 52

15 p+ 2 q 2125 p^2 - 10 pq+ 4 q 2 + 5 p- 2 q 2

1 x^2 +xy+y^221 x^2 - xy+y^22

x 4 +x^2 y^2 +y 4 x^4 +x^2 y^2 +y^4.

1 x^2 - y^221 x^4 +x^2 y^2 +y^42 ; 1 x-y 21 x+y 21 x^4 +x^2 y^2 +y^42

1 x^2 +xy+y^221 x^2 - xy+y^22

1 x-y 21 x^2 +xy+y^221 x+y 21 x^2 - xy+y^22


15 y^2 +z 2125 y^4 - 5 y^2 z+z^221 x^3 - y^321 x^3 +y^32 ;

1 m^2 - 521 m^4 + 5 m^2 + 252 13 - 10 x^3219 + 30 x^3 + 100 x^62

1 y+z+ 421 y^2 + 2 yz+z^2 - 4 y- 4 z+ 162

312 n+ 3 p 214 n 2 - 6 np+ 9 p^22

17 p+ 5 q 2149 p^2 - 35 pq+ 25 q 22

14 g- 3 h 2116 g 2 + 12 gh+ 9 h 22

15 x- 62125 x^2 + 30 x+ 362 1 x- 2 y 21 x^2 + 2 xy+ 4 y^22

110 +y 21100 - 10 y+y^2212 x+ 1214 x^2 - 2 x+ 12

16 - t 2136 + 6 t+t 22 1 x+ 421 x^2 - 4 x+ 162

1 a-b+ 422 1 x- 321 x^2 + 3 x+ 92

1 x+y- 121 x-y+ 12 217 m+ 3 n 22 1 p+q+ 122

14 m- 1 +n 214 m- 1 - n 2 12 r- 3 +s 212 r- 3 - s 2

1 p^2 + 1621 p+ 421 p- 42 1 k- 322 12 z+w 22

1 y+z+ 921 y+z- 92 14 +x+ 3 y 214 - x- 3 y 2

213 a+ 7 b 213 a- 7 b 2 414 m^2 +y^2212 m+y 212 m-y 2

1 p+ 421 p- 42 15 x+ 2215 x- 22

y^3 + 27

14 x^2 + 3214 x^2 + 12 9 x^2 - 25 p^2 + 6 pq+ 9 q 2

1 p^2 - 821 p^2 - 22 12 x^2 + 321 x^2 - 62

1 p+q 221 p+ 3 q 2 1 z-x 221 z+ 2 x 2

13 m+ 3 p+ 521 m+p- 42 1 a+b 221 a- 3 b 21 a+ 2 b 2

16 p^3 - r 212 p^3 - 5 r 2 15 k+ 4212 k+ 12

212 x+ 52 , 212 x+ 521 x- 22.

14 x+ 102

13 y 1 y+ 421 y- 12 3 p 12 p- 122

2 xy^31 x- 12 y 22 6 a 1 a- 321 a+ 52


  • 51 a+ 6213 a- 42 - 11 x 1 x- 621 x- 42


12 xz- 1213 xz+ 42 314 x+ 5212 x+ 12

14 k+ 3215 k+ 82 13 a- 2 b 215 a- 4 b 2 16 m- 522


  • 16 m- 521 m+ 32 15 x- 6212 x+ 32


1 a+ 5 b 21 a- 7 b 2 1 a- 6 b 21 a- 3 b 2

1 y- 321 y+ 102 1 p+ 821 p+ 72

Section 6.4 (pages 342–343)









  2. 7.prime 9.









































































    1. 61.prime






























Connections ( page 349) 1. 2. 3.

Section 6.5 (pages 350–354)


1.First rewrite the equation so that one side is 0. Factor the other side

and set each factor equal to 0. The solutions of these linear equations are

solutions of the quadratic equation. 3. 5.


































































      1. 47.By dividing each side by a variable expression, she “lost” the
        solution 0. The solution set is 49.







    1. 55.width: 16 ft; length: 20 ft
      57.base: 12 ft; height: 5 ft 59.50 ft by 100 ft 61. and or
      5 and 6 63.length: 15 in.; width: 9 in. 65.5 sec 67.










73.Lappears on both sides of the equation. 75.

77.

78.

ƒ 1 x 2 =- 16 x^2 + 80 x+ 100

5 - 0.5, 4 6

y=


  • x
    w- 3 , or y=


x

r= 3 - w


  • 2 k- 3 y
    a- 1 , or r=


2 k+ 3 y

1 - a

6 14 sec


  • 6 - 5


E- 32 , 154 F E- 23 , 21 F

E- 34 , 0, 34 F. E- 21 , 6F

E-^43 , 0, 34 F E- 25 , -1, 1F 5 - 3, 3, 6 6

E-^12 , 6F 5 1, 6 6 E- 21 , 0, 5F 5 - 1, 0, 3 6

5 - 2, 2 6 5 - 3, 3 6 536 E- 34 F 5 - 4, 2 6

5 - 3, 4 6 5 - 5, - 51 F 5 - 4, 0 6 5 0, 6 6

5 - 2, 5 6 5 - 6, - 36 E-^12 , 4F E- 31 , 54 F

5 - 10, 5 6 E- 38 , 25 F

5 - 1, 7 6 536 5 - 2, 2 6

1 m+n- 521 m-n+ 12 E- 32 F 506 5 - 106

12 r-t 21 r 2 - rt+ 19 t 22 1 x+ 321 x 2 + 121 x+ 121 x- 12

1 p+ 8 q- 522 17 m 2 + 1213 m^2 - 52

4 rx 13 m^2 +mn+ 10 n 22 17 a- 4 b 213 a+b 2

21 x+ 421 x- 52 8 mn 215 p+ 9215 p- 92

1 x- 2 m-n 21 x+ 2 m+n 2 6 p^313 p^2 - 4 + 2 p^32

1 m-n 21 m^2 +mn+n 2 +m+n 2

4 pq 12 p+q 213 p+ 5 q 2 314 k^2 + 9212 k+ 3212 k- 32

814 + 5 z 2116 - 20 z+ 25 z^2215 r-s 212 r+ 5 s 2

6 z 12 z^2 - z+ 32 1614 b+ 5 c 214 b- 5 c 2

1 p+ 121 p^2 - p+ 12 18 m+ 25218 m- 252

1 x+ 721 x- 52 125 +x^2215 - x 215 +x 2

13 m- 5 n 22 1 k- 921 q+r 2 16 z^2 x 1 zx- 22

9 m 1 m- 5 + 2 m^22213 m- 10219 m^2 + 30 m+ 1002

1 x- 1021 x^2 + 10 x+ 1002 1 p+ 2214 +m 2

3 pq 1 a+ 6 b 21 a- 5 b 2 16 b+ 121 b- 32

110 a+ 3 b 2110 a- 3 b 2 3 p^21 p- 621 p+ 52

A-14 Answers to Selected Exercises


–100

010

300

f(x) = –16x^2 + 80x + 100 79.200 ft; 2.5 sec 80.about 6 sec

81.in the approximate interval

82.


  1. 85.- 87.^3675
    3
    4 m^4 n^3
    4 p


1 0.7, 4.3 2 ƒ 1 x 2 =- 16 x^2 + 100 x
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