Algebra 1 Common Core Student Edition, Grade 8-9

36. q,12r4


37. a3bi 42
    37. 1.7956 38.243x3y1 16 39.
    43. 7x4 44. ,21 45.

3r10z8

o20

40. x4

81c12

46. 2 X 10“ 3 47. 2.5 X 102 48. 5 X 10“ 5


47. 3 x 103 50. Answers may vary. Sample:
    
    
    1. Simplify the expression within the parentheses.
    
    
    2. Take the reciprocal of the rational expression raised to
       the third power.
    
    
    3. Use the quotient raised to a power rule by applying the
       exponent to both the numerator and denominator.
    
    
    
    

4. Simplify the numerator.


5. Simplify the denominator using the power rule.

51. Vm 52. 53. 6x2 54.5 ^ x


52. 8 ^x 3 56.x^25Vy 57. (xy)2 58. a 4 59. b§


53. x2y3 61. 3x2 62. x§ys 63. 4, 16, 64


54. 0.01, 0.0001, 0.000001 65. 20, 10, 5


55. 6, 12, 24


56. y

X

69. y

A

/

_ X

0

70. y

X

• c

71a. 800 bacteria b. about 1.4 x 1016 bacteria

72. exponential growth; 3 73. exponential decay; 0.32


73. exponential growth; \ 75. exponential decay; \


74. $2697.20 77. 463 people 78. 2 79. 10 80. 5


75. ^ 82. a-1 — 20 , an — an—-1


76. d'j


77. d-j

5, an 3n--\

= 10 , a„ = an_!

84. a-| — 3, an —
    10

Ch ap t er 8

Get Ready! p. 483

1. 1, 2, 3, 4, 6 , 12 2. 1, 2, 3, 6 , 9 , 1 8 3. 1, 2, 4, 5, 10, 20,
   25, 50, 100 4. 1, 3, 9, 27, 81 5. 1, 2, 3, 4, 6 , 8 , 9, 12, 18,

24, 36, 72 6. 1, 2, 3, 4, 5, 6 , 10, 12, 15, 20, 25, 30, 50,

60, 75, 100, 150, 300 7. 1, 2, 5, 10, 25, 50, 125, 250

8.1,3,9,23,69,207 9. x 2 - 9x 10.3cf+ 15

11

14

24r2 - 15r 12. 34m - 29 13. -36a2 - 6 a

>2 - 7s - 2 15. 25x2 16. 9vt 17. 64c6

18. 56 mf 19. 81b6 20. 36 p2q2 21. 7n 22. -125f12


19. p 2 qr 3 24. 5x 25.^1 26. 3y 2 27. 3


20. A binomial is an expression with tw o terms.


21. b; (x + 4)(x + 4) = (x + 4)2, which is a square, and
    (x + 4)(x + 4) = x^2 +^8 x + 16, which is a trinomial.

Lesson 8-1 pp. 486-491

Go t It? 1a. 2 b. 5 c. 0 2. 5x4, - 5 x 2 y 4

3a. 8 x 2 + 2x - 3, quadratic trinomial b. Answers may

vary. Sample: Writing a polynomial in standard form

allows you to see which monomial term has the greatest

degree and how many terms the polynomial has.

4. -12x 3 + 120x 2 — 255x+ 6022
   5. -4m 3 - 4m 2 - 2m + 21
   Lesso n Ch eck 1. 4 2. 5 3. 11r 3 + 11


5. x 2 — 3x — 7 5. quadratic trinomial 6. linear
   binomial 7. The coefficient of the sum of like monomials
   is the sum of the coefficients. To add polynomials, you
   group like terms and add their coefficients. A monomial
   has only one term and a polynomial can have more than
   one term.
   Ex e r c i se s 9. 3 11. 10 13. 0 15. no degree
   17. 11m 3 n 3 19. 1414 21. 18v4w 3


6. 
   
   
   
   • 8 be 4 25. -2q + 7; linear binomial
   
   
   
   


7. -7x 2 - 4x + 4; quadratic trinomial


8. 3z 4 - 2z 2 - 5z; fourth degree trinomial


9. 9x 2 + 8 33. 2Ox 2 + 5 35. - 1 8 x 2 + 228x + 2300


10. 2x 3 + 8 39. 5b 4 + b 3 41. 9x - 1


11. The student forgot to distribute the negative sign to
    all the terms in the second set of parentheses.
    (4x 2 - x + 3) - (3x 2 - 5x - 6 ) =
    4x 2 — x + 3 - 3x 2 - (-5x) - ( - 6 ) =
    4x 2 - 3x 2 - x + 5 x + 3 + 6 =
    4x + 9 45. -5y 3 + 2y2 - 6
    3z 3 + 15z2 - 10z - 5 49. No. Answers may

x 2

47

vary. Sample: (x 2 - x + 3) + (x - x 2 + 1) = 4,

which is a monomial. 51. 14 p g 6 - 11 p4q - p 4 g 4

Lesson 8-2 pp. 492-496

Go t It? 1 .15n^4 - 5n^3 + 40n 2. 3x

3a. 3 x 2 ( 3 x 4 + 5x 2 + 4) b. - 6 x 2 (x 2 ■

4. 9x2(4 -^77 )

3x + 2)

Lesso n Ch eck 1. 12X4 + 42x2 2. 2a 2 3. 3m(2m - 5)

4. 4x(x 2 + 2x -
   Sample: 18x3

-3) 5. B 6. C

27 x2

7. A 8. Answers may vary.

C

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