Name
8-1
Class
Date
Practice
Form G
Adding and Subtracting Polynomials
Find the degree of each monomial.
1. 2b2c2 4
2. 5x 1
3. 7y5 5
4. 19ab 2
5. 12 0
1
6. 2 z2 2
7. t 1
8. 4d4e 5
Simplify.
9. 2a3b 1 4a3b 6a3b
12. 26ab 1 3ab 23ab
10. 5x3 2 4x3 x3
11. 3m6n3 2 5m6n3 22m6n3
13. 4c2d6 2 7c2d6 23c2d6
14. 315x2 2 30x2 285x2
Write each polynomial in standard form. Then name each polynomial based on
its degree and number of terms.
15. 15x 2 x3 1 3
2x3 1 15x 1 3; cubic
trinomial
18. 7b2 1 4b
7b2 1 4b; quadratic
binomial
16. 5x 1 2x2 2 x 1 3x4
3x4 1 2x2 1 4x; fourth
degree trinomial
19. 23x2 1 11 1 10x
23x2 1 10x 1 11;
quadratic trinomial
17. 9x3
9x3 ; cubic monomial
20. 12t2 1 1 2 3x 1 8 2 2x
12t2 2 5x 1 9;
quadratic trinomial
Simplify.
21.
8z 2 12
1 6z 1 90
22.
14z 2 3
24. (3k2 1 5) 1 (16x2 1 7)
9x3 1 3
1 4x3 1 7
13x3 1 10
3k2 1 16x2 1 12
23.
6j2 2 2j 1 5
1 3j 2 1 4j 2 6
9j2 1 2j 2 1
25. (g4 2 4g2 1 11) 1 (2g3 1 8g)
g4 2 g3 2 4g2 1 8g 1 11
26. A local deli kept track of the sandwiches it sold for three months. The
polynomials below model the number of sandwiches sold, where s
represents days.
Ham and Cheese:
Pastrami:
4s3 2 28s2 1 33s 1 250
27.4s2 1 32s 1 180
Write a polynomial that models the total number of these sandwiches that
were sold. 4s3 2 35.4s2 1 65s 1 430
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3
Name
Class
8-1
Date
Practice (continued)
Form G
Adding and Subtracting Polynomials
Simplify.
7x4 1 9
28.
2 (8x4 1 2)
11n 2 4
27.
2 (5n 1 2)
6n 2 6
29.
3d2 1 8d 2 2
2 (2d2 2 7d 1 6)
2x4 1 7
30. (28e3 1 3e2) 1 (19e3 1 e2)
d2 1 15d 2 8
31. (212h4 1 h) 2 (26h4 1 3h2 2 4h)
47e3 1 4e2
26h4 2 3h2 1 5h
32. A small town wants to compare the number of students enrolled in public and
private schools. The polynomials below show the enrollment for each:
Public School:
Private School:
219c2 1 980c 1 48,989
40c 1 4046
Write a polynomial for how many more students are enrolled in public school
than private school. 219c2 1 940c 1 44,943
Simplify. Write each answer in standard form.
33. (3a2 1 a 1 5) 2 (2a 2 5)
34. (6d 2 10d3 1 3d2) 2 (5d3 1 3d 2 4)
3a2 2 a 1 10
215d3 1 3d2 1 3d 1 4
35. (24s3 1 2s 2 3) 1 (22s2 1 s 1 7)
36. (8p3 2 6p 1 2p2) 1 (9p2 2 5p 2 11)
24s3 2 2s2 1 3s 1 4
8p3 1 11p2 2 11p 2 11
37. The fence around a quadrilateral-shaped pasture is
3a2 1 15a 1 9 long. Three sides of the fence have the
following lengths: 5a, 10a 2 2, a2 2 7. What is the length
of the fourth side of the fence?
5a
2a2 1 18
?
a2 ź7
10a ź2
38. Error Analysis Describe and correct the error in
simplifying the sum shown at the right.
6x3
two unlike terms,
6x3 2 3x2 1 6x 2 2
and
23x2 ,
were added;
6x3 + 4x – 10
+ (–3x2 + 2x + 8)
3x3 + 6x – 2
39. Open-Ended Write three different examples of the sum of a
quadratic trinomial and a cubic monomial.
Answers may vary. Sample: (x2 1 2x 1 1) 1 x3 ;
(2x2 1 5x 1 6) 1 3x3 ; (r2 1 r 1 1) 1 8r3
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4
Name
Class
Date
Practice
8-2
Form G
Multiplying and Factoring
Simplify each product.
1. 2x(x 1 8)
2. (n 1 7)5n
3. 6h2(7 1 h)
2x2 1 16x
5n2 1 35n
6h3 1 42h2
4. 2b2(b 2 10)
5. 23c(8 1 2c 2 c3)
2b3 1 10b2
7. 4t(t2
3c4 2 6c2 2 24c
8. 2m(4m3
2 6t 1 2)
4t3 2 24t2 1 8t
10. 2t2(2t4 1 4t 2 8)
22t6 2 4t3 1 8t2
2
8m2
6. y(2y2 2 3y 1 6)
2y3 2 3y2 1 6y
1 m)
24m4 1 8m3 2 m2
11. 2k(23k3 1 k2 2 10)
26k4 1 2k3 2 20k
13. 4v3(2v2 2 3v 1 5)
14. 5d(2d3 1 2d2 2 3d)
8v5 2 12v4 1 20v3
25d4 1 10d3 2 15d2
9. 7j(22j 2 2 8j 2 3)
214j3 2 56j2 2 21j
12. 8a2(2a7 1 7a 2 7)
28a9 1 56a3 2 56a2
15. 11w(w2 1 2w 1 6)
11w3 1 22w2 1 66w
Find the GCF of the terms of each polynomial.
16. 15x 1 27
3
17. 6w3 2 14w
2w
18. 63s 1 45
9
19. 72y5 1 18y2
20. 218q3 2 6q2
21. 108f 3 2 54
54
18y2
22. b3
1
5b2
26q2
23. 9m3 1 30m 2 24
2 20b
b
25. 2e2
3
26. 14b3
1 12e 2 22
2
28. 8a4
2p
1
21b2
2 42b
7b
1
24a3
2
40a2
29. 36j3 2 3j2 2 15j
3j
8a2
24. 4p3 1 12p2 2 18p
27. 212x3 1 24x2 2 16x
4x
30. 12j8 1 30j4 2 6j3
6j3
Factor each polynomial.
32. 18s2 1 54
31. 12x 2 9
3(4x 2 3)
18(s2 1 3)
34. 220w2 1 16w
35. 32y3 1 8y2
24w(5w 2 4)
37. 12n3 2 36n2 1 18
8y2(4y 1 1)
38. 40t3 1 25t2 1 80t
6(2n3 2 6n2 1 3)
5t(8t2 1 5t 1 16)
3c(5c3 1 8c2 2 2c 1 4)
2m(4m2 1 7m 1 3)
40. 15c4 1 24c3 2 6c2 1 12c 41. 8m3 1 14m2 1 6m
43. 36p4 1 14p3 1 35p2
p2(36p2 1 14p 1 35)
46. x6 2 x4 1 x2
x2(x4 2 x2 1 1)
44. 9a5 1 27a4 1 63a2
9a2(a3 1 3a2 1 7)
47. 34g3 1 51g2 1 17g
17g(2g2 1 3g 1 1)
33. 108t2 2 60t
12t(9t 2 5)
36. 300d2 2 175d
25d(12d 2 7)
39. 42x4 2 56x3 1 28x2
14x2(3x2 2 4x 1 2)
42. 10x2 1 50x 2 25
5(2x2 1 10x 2 5)
45. 4b4 1 20b3 1 12b
4b(b3 1 5b2 1 3)
48. 18h4 2 27h2 1 18h
9h(2h3 2 3h 1 2)
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13
Name
8-2
Class
Date
Practice (continued)
Form G
Multiplying and Factoring
49. A circular hedge surrounds a sculpture on a square base. The
radius of the hedge is 6x. The side length of the square sculpture
base is 4x. What is the area of the hedge? Write your answer in
factored form. 4x2(9π 2 4)
6x
4x
50. Suppose you are making a giant chocolate chip cookie for a raffle. You roll out
a square slab of cookie dough. Then you use a circular plate that touches the
edges of the square slab of cookie dough and cut the cookie out of the dough.
What is the area of the extra dough? Write your answer in factored form. r2(4 2 π)
Simplify. Write in standard form.
51. 23x(4x2 2 6x 1 12)
212x3 1 18x2 2 36x
54. p(p 1 4) 2 2p(p 2 8)
2p2 1 20p
57. 25m(2m3 2 7m2 1 m)
210m4 1 35m3 2 5m2
52. 27y2(24y3 1 6y)
28y5 2 42y3
55. t(t 1 4) 2 t(4t2 2 2)
24t3 1 t2 1 6t
58. 2q(q 1 1) 2 q(q 2 1)
q2 1 3q
53. 9a(23a2 1 a 2 5)
227a3 1 9a2 2 45a
56. 6c(2c2 2 4) 2 c(8c)
12c3 2 8c2 2 24c
59. 2n2(26n2 1 2n)
6n4 2 2n3
Factor each polynomial.
60. 15xy4 1 60x2y3
15xy3(y 1 4x)
63. 36j2k4 1 24j4k2
12j2k2(3k2 1 2j2)
66. 12st4 1 46s3t4
2st4(6 1 23s2)
61. 8m3n4 1 32mn2
62. 26a5b2 1 51a4
8mn2(m2n2 1 4)
a4(26ab2 1 51)
64. 12w4x3 2 42wx2
6wx2(2w3x 2 7)
67. 9v6w3 1 33v4w5
3v4w3(3v2 1 11w2)
69. Error Analysis A student factored the polynomial at the
right. Describe and correct the error made in factoring.
The student did not find the correct GCF. 7x2(9x2 2 2x 1 5)
65. 54c2d3 2 36c3d2
18c2d2(3d 2 2c)
68. 11e3f 3 1 132e2f 4
11e2f 3(e 1 12f )
63x4 – 14x3 + 35x2
= 7x(9x3 – 2x2 + 5x)
70. Reasoning The GCF of two numbers j and k is 8. What is the GCF of 2j and
2k? Justify your answer. 16 The GCF will be the product of 2 and 8.
71. A cylinder has a radius of 3m2n and a height of 7mn. The formula for the
volume of a cylinder is V 5 pr2h, where r is the radius and h is the height.
What is the volume of the cylinder? Simplify your answer. 63πm5n3
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14
Name
8-3
Class
Date
Practice
Form G
Multiplying Binomials
Simplify each product using the Distributive Property.
1. (x 1 3)(x 1 8)
2. (y 2 4)(y 1 7)
x2 1 11x 1 24
y2 1 3y 2 28
4. (c 2 6)(c 2 4)
5. (2r 2 5)(r 1 3)
3. (m 1 9)(m 2 3)
m2 1 6m 2 27
6. (3x 1 1)(5x 2 3)
c2 2 10c 1 24
2r2 1 r 2 15
15x2 2 4x 2 3
7. (d 1 2)(4d 2 3)
8. (5t 2 1)(3t 2 2)
9. (a 1 11)(11a 1 1)
4d2 1 5d 2 6
15t2 2 13t 1 2
11a2 1 122a 1 11
Simplify each product using a table.
10. (x 1 3)(x 2 5)
11. (a 2 2)(a 2 13)
x2 2 2x 2 15
a2 2 15a 1 26
13. (5h 2 3)(h 1 7)
5h2 1 32h 2 21
14. (x 2 3)(2x 1 3)
2x2 2 3x 2 9
12. (w 2 4)(w 1 8)
w2 1 4w 2 32
15. (2p 1 1)(6p 1 4)
12p2 1 14p 1 4
Simplify each product using the FOIL method.
16. (2x 2 6)(x 1 3)
2x2 2 18
17. (n 2 5)(3n 2 4)
3n2 2 19n 1 20
19. (a 1 7)(a 2 3)
20. (x 1 3)(3x 2 2)
a2 1 4a 2 21
3x2 1 7x 2 6
22. (b 2 5)(b 2 11)
23. (4m 2 1)(m 1 4)
b2 2 16b 1 55
4m2 1 15m 2 4
25. (2h 1 6)(5h 2 3)
10h2 1 24h 2 18
26. (3w 1 12)(w 1 3)
3w2 1 21w 1 36
18. (4p2 1 2)(3p 2 1)
12p3 2 4p2 1 6p 2 2
21. (k 2 9)(k 1 5)
k2 2 4k 2 45
24. (7z 1 3)(4z 2 6)
28z2 2 30z 2 18
27. (6c 2 2)(9c 2 8)
54c2 2 66c 1 16
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23
Name
Class
8-3
Date
Practice (continued)
Form G
Multiplying Binomials
x4
28. What is the surface area of the cylinder at the right? Write your
answer in simplified form.
4πx2 1 38πx 1 88π
x7
29. The radius of a cylindrical popcorn tin is (3x 1 1) in. The height
of the tin is three times the radius. What is the surface area of the
cylinder? Write your answer in simplified form.
72πx2 1 48πx 1 8π
30. The radius of a cylindrical tennis ball can is (2x 1 1) cm. The height of the
tennis ball can is six times the radius. What is the surface area of the cylinder?
Write your answer in simplified form.
56πx2 1 56πx 1 14π
Simplify each product.
31. (x 1 3)(x2 2 2x 1 4)
32. (k2 2 5k 1 2)(k 2 5)
x3 1 x2 2 2x 1 12
k3 2 10k2 1 27k 2 10
33. (3a2 1 a 1 4)(2a 2 6)
34. (2x2 1 2x 2 6)(3x 2 4)
6a3 2 16a2 1 2a 2 24
6x3 2 2x2 2 26x 1 24
35. (4g 1 5)(2g2 2 7g 1 3)
36. (m2 2 2m 1 7)(3m 1 6)
8g3 2 18g2 2 23g 1 15
3m3 1 9m 1 42
37. (2c 1 8)(2c2 2 4c 2 1)
38. (t 1 8)(3t2 1 4t 1 5)
4c3 1 8c2 2 34c 2 8
3t3 1 28t2 1 37t 1 40
39. A medical center’s rectangular parking lot currently has a length of 30 meters
and a width of 20 meters. The center plans to expand both the length and
the width of the parking lot by 2x meters. What polynomial in standard form
represents the area of the expanded parking lot?
4x2 1 100x 1 600
(2x – 3)(x + 7)
40. Error Analysis Describe and correct the error made in
x
7
2x
2x2
14x
3
3x
21
finding the product.
In the table, the 3 should be 23. Therefore, 3x should
be 23x and 21 should be 221. The answer is
2x2 1 11x 2 21.
2x2+ 17x + 21
41. Multi Step The height of a painting is twice its width x. You want
a 3 inch wide wooden frame for the painting. The area of the frame
alone is 216 square inches.
a. Draw a diagram that represents this situation.
b. Write a variable expression for the area of the frame alone.
18x 1 36
c. What are the dimensions of the frame? length is 26; width is 16
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24
2x
x
x16
2x 1 6