Algebra 1 Common Core Student Edition, Grade 8-9

insert a term with a coefficient of 0 as a placeholder.

6. Divide, multiply, subtract, bring down, and repeat as
   necessary. 7. - x 4 + Ox3 + Ox2 + Ox + 1
   Ex e r c i se s 9. 3x4 - \ 11. n2 - 18n + 3
   11
   7
   22


7. f3 + 2 l2 — 41 + 5 15. 3l2 + y -


8. y - 3 + Ff y 19,


9. 2w2 + 2w + 5 - w_ 1


10. 4c2 - 8 c + 16 27. a - 1

2(? 1 0 '' 2q + 1

10 2 3. c 2------—

1

29. 1+ 5 2f

4a + 7

^6 31. 4g 2 + 2g + 1

33. 4c 2 + 9c + 7 , 3c_ 4^36 v
    35.3y 2 + 5y + f + 3 ^ 5 ) 3 7. 2 x + 2


34. 513 - 2 5 l 2 + 1 1 5 1 - 575 +


35. 3s - 8 + 2^3 43. 2r4 + r2 - 7


36. z3 - 3 z 2 + 1 0 Z -3 0 +z + 3


37. 6m2 - 24m + 99 - 49. m 2 + 5m + 4
    301 , 1703 , 891
    200 ^ 400 ^ 400(2s + 3)53a. t = j
    b. (I2 - 7 1 + 12) h 55. (x8 + 1 Xx4 + 1 )(x2 + 1 )(x + 1);
    factoring is much simpler and faster, since long division
    requires writing a polynomial with 17 terms. 57. (3x+ 2)


38. 2 b3 - 2 b 2 + 3 61. G 63. There are 18 • 28 = 504
    seats in the theater. If 445 adults were at the theater, the
    revenue would be 445 * 4 = 1780. That means the
    revenue for the children's tickets is 1935 - 1780 = 155.
    So the number of children's seats sold is 155 a- 2.5 = 62.
    The total number of seats sold would be 62 + 445 = 507.
    Since 507 > 504, Barbara's answer is not reasonable.


39. n + 2 65,(t- 5)(3t+ 1)(2t+ 11)3f(2f - 55)(f + 1)


40. j* + (x + 7)(x + 8)2 75!! X + % 68- | 69- 3 -J2 12
    Lesson 11-4

66.3c + 8 2c + 7

70.x 71. £

pp. 684-689

Go t It? 1 3a - 4 5a 2a.z + 3

-2 - 14c + 4 45 h 4 m.

(3 c - 1 )(c — 2 ) 4 r D - 5

Sn-2

45

q-2
; if n is the
miles per gallon when the truck is full, then m = 1.25/7
and therefore n = ^ or

Lesso n Ch eck 1.x - 7^11 ’ y + 2 ■ 24b3 ’ 3r16b ■^10

5. If the expressions have like denominators, add or
   subtract numerators as indicated and place over the
   denominator. If they have unlike denominators, factor if
   needed, find the LCD, rewrite the expressions with the
   common denominator, add or subtract as indicated, and
   simplify. 6. The procedure is the same. The LCD is the
   LCM of the denominators. 7a. yes b. No, it will give you
   a common denominator, but not necessarily the least
   common denominator.

Ex e r c i se s 9. ^^14 1 1. 6 c - 2 8 1 3. -^1 ,^1 15.^2

17. 2x2 19. 7z 21. 5(x + 2) 23. (m + n)(m - n)

25.

31

35 + 6 a

15 a 27,

a2 + 12a + 15

189 - 9n

7 n3

33a. 1

29.(a + 4)(a - 3)

r + 0.7 r

(,a + 3 )(a + 5)

J--JLZ. u I!

4(a + 3) OJr ° m Ir

c. about 0.81 h or 48.6 min 35. Not always; the

numerator may contain a factor of the LCD.

37 -yz + 2y+2 ,n r - 2k -^6 10x+15

43

49

3y+ 1

5000r+ 250,000

39.

r(r + 100)

51. ~4x

45

9 + p 3

8x2 + 1

3 + xy53.

Lesson 11-5

3 b

x

3y + 4x

2y - 3x

41.

47.

x + 2

—3x - 5

x(x - 5)

Go t It? 1a.

expression ^

2a. -I 2-

pp. 691-697

(^37) 7 “ *■ 2' 3b. -7, -1 c. The
cannot be negative. 3. 4.8 h 4a. -8
b. -3, 7 5. 0
Lesso n Ch eck 1 .- 1 2. 1, 5 3. 0 4. about 28 min

5. An extraneous solution of a rational equation is an
   excluded value of the associated rational function.


6. Answers may vary. Sample: y y = y


7. The student forgot to first multiply both sides of the
   equation by the LCD, 5m.
   Ex e r c i se s 9. 3 11. -1 ,6 13. -2 15. 5 17. -2, 4


8. -y 21. — 1 23. 1 j h 25. 3 27. -f, 4 29. no solution


9. You could rewrite the right side of the equation as
   y y and then cross multiply. 33. -14 35. -5, 2


10. -f, -1 39. 12 h
    41a.-----“ b. (-9 .5 3 , 1.07),
    (-4 .1 6 , 1.35),
    (- 1 .1 2 , 5.76),
    (0.81, 10.16)

c. Yes; the x-values are solutions to the original equation

since both sides are equal. 43. 20 fl 45. 11 y h 47. 0, \

49. 1 51. 32 L of 80% solution, 18 L of 30% solution
    30 m 1 h
    1 h ’ 3 6 0 0 S
    3b2 + 2ht + 4h


50. F 55.

57: 2(t - 2)(f + 2) 58.

« = 44 ft/s 1 mi ' 56. —x2y2zyT

-4k - 61

(k-4)(k+ 10)

y

/ X

0

c

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