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Beginning Algebra, 11th Edition

(Marvins-Underground-K-12) #1

























  5. 91.commutative property

  6. 93.No, because it is not a product.
    It is the difference between and.

  7. ; yes 95. 97.




Section 6.2 (pages 371–373)


1.1 and 48, and , 2 and 24, and , 3 and 16, and ,
4 and 12, and , 6 and 8, and ; The pair with a sum of
is and. 3.1 and , and 24, 2 and , and 12,
3 and , and 8, 4 and , and 6; The pair with a sum of is
3 and. 5.aandbmust have different signs, one positive and one
negative. 7.A prime polynomial is a polynomial that cannot be factored
by using only integers in the factors. 9.C 11.

































    1. 33.prime







      1. 41.prime 43. 45.






















































Section 6.3 (pages 378–380)













  2. (a)2, 12, 24, 11 (b)3, 8 (Order is irrelevant.) (c) 3 m, 8m
    (d) (e)
    (f ) 9.B 11.B 13.A



    1. ; , , or ,



  4. ;
    21.The binomial cannot be a factor because its terms have a
    common factor of 2, which the polynomial terms do not have.



















  8. 37.prime 39.





































  15. 118 x^2 - 5 y 212 x^2 - 3 y 2 67. 2124 a+b 21 a- 2 b 2


112 x+ 121 x- 42 124 y+ 7 x 21 y- 2 x 2

13 x+ 421 x+ 42 - 5 x 12 x+ 721 x- 42

m^4 n 13 m+ 2 n 212 m+n 2 1 x- 521 x- 12

15 a+ 3 b 21 a- 2 b 2 14 s+ 5 t 213 s-t 2

3 n^215 n- 321 n- 22 y^215 x- 4213 x+ 12

314 x- 1212 x- 32 q 15 m+ 2218 m- 32

14 y+ 1215 y- 112 215 x+ 3212 x+ 12

15 m- 4212 m- 32 14 w- 1212 w- 32

13 m- 1215 m+ 22 13 s- 1214 s+ 52

13 a+ 721 a+ 12 12 y+ 321 y+ 22

2 x- 6

2 z^2 - 5 z- 32 z+1,z-3, or z-3, 2z+ 1

2 a+ 5 b x^2 + 3 x- 4 x+ 4 x- 1 x- 1 x+ 4

12 m+ 321 m+ 42 = 2 m^2 + 11 m+ 12

2 m^2 + 3 m+ 8 m+ 12 12 m+ 321 m+ 42

12 t+ 1215 t+ 22 13 z- 2215 z- 32 12 s-t 214 s+ 3 t 2

12 p+q 21 r- 921 r- 32 2 y^2 +y- 28 15 z^2 - 4 z- 4

z^81 z- 7 y 21 z+ 3 y 2 1 a+b 21 x+ 421 x- 32

a^31 a+ 4 b 21 a-b 2 yz 1 y+ 3 z 21 y- 2 z 2

5 m^21 m^3 + 5 m^2 - 82 mn 1 m- 6 n 21 m- 4 n 2

41 x+ 521 x- 22 2 t 1 t+ 121 t+ 32 2 x^41 x- 321 x+ 72

1 t+ 2 z 21 t- 3 z 2 1 x+y 21 x+ 3 y 2 1 v- 5 w 21 v- 6 w 2

1 x+ 1621 x- 22 1 r+ 2 a 21 r+a 2

1 z- 721 z- 82 1 r- 621 r+ 52 1 a+ 421 a- 122

1 m+ 521 m- 42 1 y- 521 y- 32

y- 9 1 y+ 821 y+ 12 1 b+ 321 b+ 52

p+ 6 x+ 11 x- 8 y- 5 x+ 11

a^2 + 13 a+ 36


  • 8

  • 8 - 3 - 6 - 4 - 5

  • 3 - 16 - 24 - 1 - 12 - 2

  • 4 - 12 - 6 - 8 - 19

  • 1 - 48 - 2 - 24 - 3 - 16


2 x^4 + 6 x^3 + 10 x^2

12 x- 321 y- 42 x^2 - 3 x- 54 x^2 + 9 x+ 14

2 x 1 y- 42 31 y- 42

2 x 1 y- 42 - 31 y- 42

11 + 2 b 21 a^5 - 32

15 - 2 p 21 m+ 32 13 r+ 2 y 216 r-t 2

14 m-p^2214 m^2 - p 2 1 y+ 321 y+x 2

1 a^2 +b^2213 a+ 2 b 2 13 - a 214 - b 2

1 z+ 2217 z-a 2 13 r+ 2 y 216 r-x 2 69. 71.
























      1. , 4





  5. , , 7, 11 93. 95.


Section 6.4 (pages 387–389)

1.1; 4; 9; 16; 25; 36; 49; 64; 81; 100; 121; 144; 169; 196; 225; 256;

289; 324; 361; 400 3.1; 8; 27; 64; 125; 216; 343; 512; 729; 1000


  1. (a)both of these (b)perfect cube (c)perfect square
    (d)perfect square 7. 9.
    11.prime 13. 15.







  3. 23.prime 25.







  5. can be factored as. The completely factored
    form is. 33. 10 35. 9 37.


































































































Summary Exercises on Factoring (pages 390–391)

1.G 2.H 3.A 4.B 5.E 6.I 7.C 8.F 9.I 10.E










































































































  13. 7 k 12 k+ 521 k- 22 44. 15 +r 211 - s 2


13 k- 221 k+ 22 15 a^3 b^213 b^3 - 4 a+ 5 a^3 b^22

613 m+ 2 z 213 m- 2 z 2 14 m- 3212 m+ 12

112 x- 121 x+ 42 12 k- 322 18 p- 121 p+ 32

13 y- 4212 y+ 12 1 m+ 921 m- 92 16 z+ 121 z+ 52

13 y- 1213 y+ 52 414 x+ 52 1 m+ 521 m- 32

10 nr 110 nr+ 3 r^2 - 5 n 2 13 n- 2212 n- 52

1 z- 5 a 21 z+ 2 a 2 501 z^2 - 22 1 x- 521 x- 42

513 y+ 12 8 a^31 a- 321 a+ 22 14 k+ 1212 k- 32

15 z- 6212 z+ 12 21 m- 821 m+ 32 17 xy 1 x^2 y+ 32

1 m- 4 n 21 m+n 2 1 p- 1121 p- 62 1 z+ 721 z- 62

7 y^41 y+ 621 y- 42 61 a+ 2 b+ 3 c 2

1 a- 621 a+ 22 1 a+ 821 a+ 92 61 y- 221 y+ 12

1 m-p+ 221 m+p 2 546 5 - 56

1 x-0.5 (^22) Ax+ 21 BAx^2 -^12 x+ 41 B 4 mn
A^6 m+^45 BA^6 m-^45 B^1 x+0.8^21 x-0.8^2 At+ 21 B^2
1 x+y 21 x^2 - xy+y^221 x^6 - x^3 y^3 +y^62 Ap+ 31 BAp- 31 B
13 m^2 + 2 n 219 m^4 - 6 m^2 n+ 4 n^22
12 x- 5 y^2214 x^2 + 10 xy^2 + 25 y^42
15 t+ 2 s 2125 t^2 - 10 ts+ 4 s^22
13 a+ 4 b 219 a^2 - 12 ab+ 16 b^22
12 p+ 9 q 214 p^2 - 18 pq+ 81 q^22
21 x- 2 y 21 x^2 + 2 xy+ 4 y^22
51 x+ 221 x^2 - 2 x+ 42 1 y- 2 x 21 y^2 + 2 yx+ 4 x^22
13 x- 4219 x^2 + 12 x+ 162 61 p+ 121 p^2 - p+ 12
1 m+ 221 m^2 - 2 m+ 42 1 k+ 1021 k^2 - 10 k+ 1002
z^2125 z^2 + 5 z+ 12 1 a- 121 a^2 +a+ 12
18 x+ 3 y 22 215 h- 2 y 22 k 14 k^2 - 4 k+ 92
1 x- 422 21 x+ 622 14 x- 522 17 x- 2 y 22
1 k^2 + 921 k+ 321 k- 32 1 w+ 122
k^2 - 9 1 k+ 321 k- 32
1 x^2 + 121 x+ 121 x- 12 1 p^2 + 1621 p+ 421 p- 42
14 r+ 5 a 214 r- 5 a 2 1 p^2 + 721 p^2 - 72
413 x+ 2213 x- 22 114 p+ 152114 p- 152
41 m^2 + 42 13 r+ 2213 r- 22
1 y+ 521 y- 52 1 x+ 1221 x- 122



  • 11 - 7 49 p^2 - 9 x^2 + 12 x+ 36


1 m+ 12315 q- 2215 q+ 12 1 r+ 32313 x+ 2 y 22 - 4


  • 113 x+ 421 x- 12 - 11 a+ 2 b 212 a+b 2


14 x+ 3 y 216 x+ 5 y 2 - 11 x+ 721 x- 32

112 x- 5212 x- 32 18 x^2 - 3213 x^2 + 82

x^2 y^5110 x- 121 x+ 42 4 ab^219 a+ 121 a- 32

Answers to Selected Exercises A-15
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