Name CHAPTER
8
Date
Class
Chapter Test Form A 2 8. Factor x ⫹ 12x ⫹ 35. A x ⫹ 1 x ⫹ 35 B x ⫹ 5 x ⫹ 7
Select the best answer. 1. Which is the prime factorization of 24? A 2⭈2⭈2⭈3 B 4⭈6
9. Factor x 2 ⫺ 23x ⫹ 22. A x ⫺ 2 x ⫺ 11 B x ⫺ 1 x ⫺ 22 C x ⫹ 1 x ⫺ 23 D cannot be factored
2. Find the GCF of 12 and 30. A 2 C 6 B 3 D 36 3. Find the GCF of 5x 3 and 15x. A 5x C 15x 3 B 5x D 15x 3
10. Factor x 2 ⫹ 13x ⫺ 13. A x ⫺ 1 x ⫹ 13 B x ⫺ 1 x ⫹ 14 C x ⫹ 1 x ⫹ 12 D cannot be factored
4. Shadé is organizing the members of a chorus into rows for a performance. The chorus consists of 70 women and 42 men. Each row will have the same number of people, but women and men will not appear in the same row. If she puts the greatest possible number of people in each row, how many rows will there be? A 8 B 14
11. Which value of b would make x 2 ⫹ bx ⫺ 16 factorable? A ⫺10 B ⫺6 12. Write the factored form of the polynomial that is modeled by this geometric diagram.
5. Factor 16y 2 ⫹ 12y completely. A y 16y ⫹ 12 B 2y 8y ⫹ 6 C 4 4y 2 ⫹ 3y D 4y 4y ⫹ 3
X
X
X
6. Factor n n ⫹ 2 ⫹ 7 n ⫹ 2 . A n ⫹ 2 n ⫹ 7 B 2 n ⫹ 2 n ⫹ 7
A B C D
7. Factor a ⫹ 3a ⫹ 8a ⫹ 24 by grouping. A a ⫹ 3 a ⫹ 8 B a 2 ⫹ 3a 8a ⫹ 24 C 8a a ⫹ 3 D cannot be factored 2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 147
147
x ⫹ 1 x ⫹ 8 x ⫹ 2 x ⫹ 4
x 2 ⫹ 4x 2x ⫹ 8 2x ⫹ 8 4x ⫹ 8
Holt Algebra 1
1/3/06 6:15:12 PM Process Black
Name
Date
CHAPTER
Chapter Test
8
Form A continued 19. Determine whether x 2 ⫺ 16 is a difference of two squares. If so, choose the correct factorization. A yes; x ⫺ 4 2
13. Factor 2x 2 ⫹ 23x ⫹ 11. A x ⫹ 1 2x ⫹ 11 B 2x ⫹ 1 x ⫹ 11 14. Factor 5a 2 ⫺ 3a ⫺ 2. A a ⫺ 2 5a ⫹ 1 B a ⫺ 1 5a ⫹ 2 C a ⫹ 1 5a ⫺ 2 D cannot be factored
B yes; x ⫹ 4 x ⫺ 4 C yes; x ⫹ 4 2 D no 20. The area of a square is represented by z 2 ⫹ 10z ⫹ 25. Which expression represents the perimeter of the square? A z⫹5 B z⫹9 C 2z ⫹ 10 D 4z ⫹ 20
15. Which value of c would NOT make 2x 2 ⫹ 5x ⫹ c factorable? A ⫺2 B ⫺3 16. Determine whether n 2 ⫹ 20n ⫹ 100 is a perfect square trinomial. A yes B no
21. Is 5x x 2 ⫹ 36 completely factored? A yes; the polynomial is completely factored. B no; x 2 ⫹ 36 can be factored into two binomials.
17. Determine whether x 2 ⫺ 6x ⫺ 9 is a perfect square trinomial. If so, choose the correct factorization. A yes; x ⫺ 3 2 B yes; x ⫹ 3 2 C yes; x ⫹ 3 x ⫺ 3 D no
22. Completely factor x 4 ⫹ 2x 3 ⫺ 15x 2. A x 2 ⫹ 5x x 2 ⫺ 3x B x 2 x ⫹ 5 x ⫺ 3 23. Completely factor 4m 4 ⫺ 324. A 4m 2 ⫹ 36 m 2 ⫺ 9 B 4 m 2 ⫹ 9 m ⫹ 3 m ⫺ 3 C 4 m ⫹ 3 2 m ⫹ 3 m ⫺ 3 D cannot be factored
18. Determine whether p ⫺ 40 is a difference of two squares. A yes B no 2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 148
Class
148
Holt Algebra 1
1/3/06 6:15:13 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form B 2 8. Factor x ⫹ 8x ⫹ 12. F x ⫹ 1 x ⫹ 12 G x ⫹ 2 x ⫹ 6 H x ⫹ 3 x ⫹ 4 J cannot be factored
Select the best answer. 1. Which is the prime factorization of 120? A 2 ⭈ 2 ⭈ 2 ⭈ 15 C 3⭈5⭈8 B 2⭈2⭈2⭈3⭈5 D 10 ⭈ 12 2. Find the GCF of 42 and 70. F 7 H 196 G 14 J 210
9. Factor x 2 ⫺ 3x ⫹ 70. A x ⫺10 x ⫹ 7 B x ⫺ 7 x ⫺ 10 C x ⫹ 5 x ⫹ 14 D cannot be factored
3. Find the GCF of 30x 2 and 45x 5. A 5x 2 C 15x 2 B 5x 5 D 15x 5
10. Factor x 2 ⫺ 6x ⫺ 16. F x ⫺ 2 x ⫺ 8 G x ⫺ 2 x ⫹ 8 H x ⫹ 2 x ⫺ 8 J cannot be factored
4. Kyle is making flower arrangements for a wedding. He has 16 roses and 60 carnations. Each arrangement will have the same number of flowers, but roses and carnations will not appear in the same arrangement. If he puts the greatest possible number of flowers in each arrangement, how many arrangements can he make? F 4 H 19 G 15 J 38
11. Which value of b would make x 2 ⫹ bx ⫺ 30 factorable? A ⫺31 C 11 B ⫺17 D 13 12. Write the factored form of the polynomial that is modeled by this geometric diagram.
5. Factor 30y ⫺ 6y ⫹ 12y completely. A y 30y 2 ⫺ 6y ⫹ 12 B 3y 10y 2 ⫺ 2y ⫹ 4 C 6 5y 3 ⫺ y 2 ⫹ 2y D 6y 5y 2 ⫺ y ⫹ 2 3
2
6. Factor 2n n ⫹ 3 ⫺ 5 n ⫹ 3 . F n ⫺ 3 2n ⫹ 5 G n ⫹ 3 2n ⫹ 5 H n ⫹ 3 2n ⫺ 5 J cannot be factored
a107c08_Assess.indd 149
X
X
F x ⫹ 3 12x ⫹ 1 G 2x ⫹ 3 6x ⫹ 1 H 3x ⫹ 1 4x ⫹ 3 J 12x 2 ⫹ 4x 9x ⫹ 3
7. Factor 6a 3 ⫺ 3a 2 ⫹ 8a ⫺ 4 by grouping. A 2a ⫺ 1 3a 2 ⫹ 4 B 2a ⫹ 4 3a 2 ⫺ 1 C 6a 3 ⫺ 3a 2 8a ⫺ 4 D cannot be factored
Copyright © by Holt, Rinehart and Winston. All rights reserved.
X
149
Holt Algebra 1
1/3/06 6:15:14 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form B
continued
13. Factor 5x ⫹ 39x ⫹ 54. A x ⫹ 2 5x ⫹ 27 B x ⫹ 3 5x ⫹ 18 C x ⫹ 6 5x ⫹ 9 D cannot be factored
2 19. Determine whether 4x ⫺ 10 is a difference of two squares. If so, choose the correct factorization. 2 A yes; 2x ⫺ 5 B yes; 2x ⫹ 5 2x ⫺ 5 C yes; 2x ⫹ 10 2x ⫺ 10 D no
2
2 14. Factor 8a ⫺ 10a ⫺ 7. F 2a ⫺ 7 4a ⫹ 1 G 2a ⫺ 1 4a ⫹ 7 H 2a ⫹ 1 4a ⫺ 7 J cannot be factored
20. The area of a square is represented 2 by 9z ⫺ 12z ⫹ 4. Which expression represents the perimeter of the square? F 3z ⫺ 2 H 6z ⫺ 4 G 3z ⫹ 2 J 12z ⫺ 8
15. Which value of c would NOT make 2 3x ⫹ 5x ⫹ c factorable? A ⫺22 C 2 B ⫺2 D 22
2 21. Is x 4x ⫹ 8x ⫹ 12 completely factored? If not, what other factoring can occur? A yes; the polynomial is completely factored. B no; 4 can be factored from each term of the trinomial. 2 C no; the trinomial 4x ⫹ 8x ⫹ 12 can be factored into two binomials. D no; 4 can be factored from each term of the trinomial AND the resulting trinomial can be factored into two binomials.
2 16. Determine whether n ⫺ 10n ⫺ 25 is a perfect square trinomial. If so, choose the correct factorization. 2 F yes; n ⫺ 5 G yes; n ⫹ 5 2 H yes; n ⫹ 5 n ⫺ 5 J no 2 17. Determine whether 16x ⫹ 24x ⫹ 9 is a perfect square trinomial. If so, choose the correct factorization. 2 A yes; 4x ⫺ 3 B yes; 4x ⫹ 3 2 C yes; 4x ⫹ 3 4x ⫺ 3 D no
22. Completely factor 4 3 2 3x ⫺ 15x ⫺ 18x . 2 F x 3x ⫹ 2 1x ⫺ 9 2 2 G 3 x ⫹ 1 x ⫺ 6 2 H 3x x ⫹ 1 x ⫺ 6 J cannot be factored
2 18. Determine whether p ⫺ 36 is a difference of two squares. If so, choose the correct factorization. 2 F yes; p ⫺ 6 G yes; p ⫹ 6 p ⫺ 6 H yes; p ⫹ 18 p ⫺ 18 J no
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 150
23. Completely factor 3 2 3m ⫹ 5m ⫺ 12m ⫺ 20. A m 2 ⫺ 4 3m ⫹ 5 B m ⫺ 2 2 3m ⫹ 5 C m 2 ⫹ 4 3m ⫹ 5 D m ⫹ 2 m ⫺ 2 3m ⫹ 5
150
Holt Algebra 1
5/23/06 4:09:03 PM
Name CHAPTER
8
Date
Class
Chapter Test Form C 2 8. Factor x ⫹ 29x ⫹ 210. F x ⫹ 6 x ⫹ 35 G x ⫹ 10 x ⫹ 21 H x ⫹ 14 x ⫹ 15 J cannot be factored
Select the best answer. 1. Which is the prime factorization of 2040? A 2 3 ⭈ 3 ⭈ 5 ⭈ 17 C 8 ⭈ 15 ⭈ 17 3 B 2 ⭈ 5 ⭈ 51 D 40 ⭈ 51 2. Find the GCF of 330 and 2100. F 3 H 30 G 5 J 60
9. Factor x 2 ⫺ 13x ⫺ 30. A x ⫺ 3 x ⫺ 10 B x ⫹ 1 x ⫺ 30 C x ⫹ 2 x ⫺ 15 D cannot be factored
3. Find the GCF of 30x 2 and 105y 2. A 5 C 15 2 2 B 5x y D 15x 2y 2
10. Factor x 2 ⫹ 21x ⫺ 54. F x ⫺ 3 x ⫺ 18 G x ⫺ 3 x ⫹ 18 H x ⫹ 3 x ⫺ 18 J cannot be factored
4. Carlos is planting a vegetable garden. He has 30 carrot seeds, 24 tomato seeds, and 36 lettuce seeds. Each row will have the same number seeds, but carrots, tomatoes, and lettuce will not appear in the same row. If he puts the greatest possible number of seeds in each row, how many rows will there be? F 5 H 15 G 6 J 30
11. Which value of b would make x 2 ⫹ bx ⫹ 36 factorable? A ⫺20 C 5 B ⫺9 D 35
5. Factor ⫺3y 3 ⫺ 6y 2 ⫹ 2y completely. A ⫺3y y 2 ⫹ 2y ⫹ 2 B ⫺y 3y 2 ⫺ 6y ⫹ 2 C ⫺y 3y 2 ⫹ 6y 2 ⫺ 2 D ⫺3 y 3 ⫺ 2y 2 ⫺ 2
12. Write the factored form of the polynomial that is modeled by this geometric diagram.
6. Factor 2n 5n ⫹ 3 ⫹ 7 5n ⫺ 3 . F 2n ⫹ 7 5n ⫹ 3 G 2n ⫺ 7 5n ⫹ 3 H ⫺1 2n ⫺ 7 5n ⫺ 3 J cannot be factored
a107c08_Assess.indd 151
X
X
F G H J
7. Factor 8a 3 ⫺ 6a 2 ⫹ 3 ⫺ 4a by grouping. A 2a 2 ⫺ 1 4a ⫺ 3 B 2a 2 ⫹ 1 4a ⫺ 3 C ⫺1 2a 2 ⫹ 1 4a ⫺ 3 D cannot be factored
Copyright © by Holt, Rinehart and Winston. All rights reserved.
X
151
2x ⫺ 9 4x ⫹ 3 x ⫺ 9 8x ⫹ 3 x ⫹ 3 8x ⫺ 9 2x ⫹ 3 4x ⫺ 9
Holt Algebra 1
1/3/06 6:15:16 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form C
continued
13. Factor 18x 2 ⫹ 39x ⫹ 20. A x ⫹ 1 18x ⫹ 20 B 2x ⫹ 5 9x ⫹ 4 C 3x ⫹ 4 6x ⫹ 5 D cannot be factored
2 16 19. Determine whether 14x ⫺ 25y is a difference of two squares. If so, choose the correct factorization. 2 A yes; 7x ⫺ 5y 4
B yes; 7x ⫹ 5y 4 7x ⫺ 5y 4 C yes; 7x ⫹ 5y 8 7x ⫺ 5y 8 D no
14. Factor 20a 2 ⫺ 144a ⫺ 45. F 2a ⫺ 15 10a ⫺ 3 G 2a ⫺ 15 10a ⫹ 3 H 2a ⫹ 15 10a ⫺ 3 J cannot be factored
20. The area of a square is represented by 81z 2 ⫹ 306z ⫹ 289. Which expression represents the perimeter of the square? F 9z ⫹ 17 H 18z ⫹ 34 G 9z ⫹ 21 J 36z ⫹ 68
15. Which value of c would NOT make 6x 2 ⫺ 13x ⫹ c factorable? A ⫺5 C 2 B ⫺2 D 5
21. Is x 4x 2 ⫺ 16 completely factored? If not, what other factoring can occur? A yes; the polynomial is completely factored. B no; 4 can be factored from each term of the binomial. C no; the binomial is a difference of two squares and can be factored into two binomials. D no; 4 can be factored from each term of the binomial AND the resulting binomial is a difference of two squares that factors into two binomials.
16. Determine whether 25n 2 ⫹ 140n ⫹ 196 is a perfect square trinomial. If so, choose the correct factorization. F yes; 5n ⫺ 14 2 G yes; 5n ⫹ 14 2 H yes; 5n ⫹ 14 5n ⫺ 14 J no 17. Determine whether 9x 2 ⫺ 120x ⫺ 400 is a perfect square trinomial. If so, choose the correct factorization. A yes; 3x ⫺ 20 2
22. Completely factor 9x 4 ⫹ 15x 3 ⫹ 2. 2 2 F 3x 3x ⫹ 5x ⫹ 2 2 G 3x 3x ⫹ 2 x ⫹ 1 2 2 H 9x ⫹ 1 x ⫹ 2 J cannot be factored
B yes; 3x ⫹ 20 2 C yes; 3x ⫹ 20 3x ⫺ 20 D no 18. Determine whether 9p 2 ⫺ 225 is a difference of two squares. If so, choose the correct factorization. F yes; 3p ⫹ 15 2
23. Completely factor 4m 4 ⫺ 16m 2 ⫹ 100 ⫺ 25m 2. A m 2 ⫺ 4 4m 2 ⫺ 25 B m ⫹ 2 m ⫺ 2 4m 2 ⫹ 25 C m ⫹ 2 m ⫺ 2 2m ⫺ 5 2m ⫹ 5 D 4m 2 m 2 ⫺ 4m ⫹ 25
G yes; 3p ⫺ 15 2 H yes; 3p ⫹ 15 3p ⫺ 15 J no
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 152
152
Holt Algebra 1
1/3/06 6:15:17 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form A 7. Factor a 3 ⫺ 5a 2 ⫹ 2a ⫺ 10 by grouping.
1. Write the prime factorization of 36.
Find the GCF.
Factor each trinomial.
2. 8 and 28
8. x 2 ⫹ 10x ⫹ 21
3. 6x 2 and 18x 5
9. x 2 ⫺ 3x ⫺ 10
10. x 2 ⫹ 16x ⫺ 55
4. Marlon is putting his stamp collection in a new album. He has 20 stamps from Canada and 90 stamps from the U.S. Each page of the album will have the same number of stamps, but stamps from Canada and the U.S. will not appear on the same page. If he puts the greatest possible number of stamps on each page, how many pages will he use?
11. Find an integer value of b that makes x 2 ⫹ bx ⫺ 15 factorable, and then factor the trinomial.
b⫽
Factor.
12. Write the polynomial modeled by this geometric diagram and then factor.
5. 30y 3 ⫺ 50y
6. n n ⫺ 3 ⫹ 8 n ⫺ 3
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 153
153
X
X
X
Holt Algebra 1
1/3/06 6:15:18 PM Process Black
Name
Date
CHAPTER
Chapter Test
8
Form A continued
Class
19. x 2 ⫺ 100
Factor each trinomial. 13. 7x 2 ⫹ 29x ⫹ 4
14. 3a 2 ⫺ 4a ⫺ 7 20. The area of a square in square feet is represented by z 2 ⫹ 12z ⫹ 36. Find an expression for the perimeter of the square. Then find the perimeter when z ⫽ 4 ft.
15. Determine whether each value of c makes 3x 2 ⫹ 7x ⫹ c factorable. If so, factor it. c ⫽ ⫺2
expression:
c⫽2
perimeter when z ⫽ 4 ft: 21. Tell whether 8x ⫺ 5 4x ⫹ 12 is completely factored. If not, factor it.
Determine whether the trinomial is a perfect square. If so, factor it. If not, explain why. 16. n 2 ⫹ 50n ⫹ 25
17. x 2 ⫺ 18x ⫹ 81
Factor each polynomial completely. 22. 5x 3 ⫹ 40x 2 ⫺ 100x
Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why.
23. 3m 4 ⫺ 48
18. p 2 ⫺ 30
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 154
154
Holt Algebra 1
1/3/06 6:15:18 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form B 7. Factor 15a 3 ⫹ 20a 2 ⫺ 6a ⫺ 8 by grouping.
1. Write the prime factorization of 176.
2 4 ⭈ 11
3a
ⴙ 4 5a 2 ⴚ 2
Find the GCF. Factor each trinomial.
2. 54 and 144
2 8. x ⫹ 9x ⫹ 18
18
ⴙ 6 x ⴙ 3
x
3. 30x 2 and 66x 5
9. x 2 ⫹ 7x ⫺ 30
6x 2
x
4. Mrs. Mendoza is organizing seating for a standardized test. 45 ninth-grade students and 120 tenth-grade students will take the test. Each row will have the same number of students, but ninthgraders and tenth-graders will not be seated in the same row. If she puts the greatest possible number of students in each row, how many rows will there be?
10. x 2 ⫺ 5x ⫺ 50
x
b⫽
Possible answer: 43 x
Factor.
ⴙ 1 x ⴙ 42
12. Write the polynomial modeled by this geometric diagram and then factor.
3 2 5. 14y ⫹ 28y ⫺ 54y
2y 7y 2 ⴙ 14y ⴚ 27 6. n 2n ⫹ 3 ⫹ 4 2n ⫺ 3
X
X
X
18x 2 ⴙ 21x ⴙ 5 ⴝ 3x ⴙ 1 6x ⴙ 5
cannot be factored
a107c08_Assess.indd 155
ⴙ 5 x ⴚ 10
11. Find an integer value of b that makes 2 x ⫹ bx ⫹ 42 factorable, and then factor the trinomial.
11 rows
Copyright © by Holt, Rinehart and Winston. All rights reserved.
ⴚ 3 x ⴙ 10
155
Holt Algebra 1
5/4/06 4:40:52 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form B
continued 19. 16x 2 ⫺ 49
Factor each trinomial. 13. 3x 2 ⫹ 47x ⫹ 140
yes x
ⴙ 4 3x ⴙ 35
4x
14. 27a 2 ⫹ 42a ⫺ 5
3a
20. The area of a square in square feet is represented by 4z 2 ⫺ 36z ⫹ 81. Find an expression for the perimeter of the square. Then find the perimeter when z ⫽ 10 ft.
ⴙ 5 9a ⴚ 1
15. Determine whether each value of c makes 5x 2 ⫺ 22x ⫹ c factorable. If so, factor it. c ⫽ ⫺15 c⫽4 c⫽8
ⴙ 7 4x ⴚ 7
ⴚ 5 5x ⴙ 3 cannot be factored x ⴚ 4 5x ⴚ 2 x
8z ⴚ 36 44 ft perimeter when z ⫽ 10 ft: expression:
21. Tell whether x 4x 2 ⫹ 19x ⫹ 12 is completely factored. If not, factor it.
Determine whether the trinomial is a perfect square. If so, factor it. If not, explain why.
no
16. n 2 ⫹ 72n ⫹ 36
x x ⴙ 4 4x ⴙ 3
no 72n ⴝ 2 n ⭈ 6 17. 9x 2 ⫺ 30x ⫹ 25
Factor each polynomial completely. 22. 4x 5 ⫺ 30x 4 ⫺ 16x 3
yes 3x
ⴚ 5 2 3 2x x ⴚ 8 2x ⴙ 1
Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why.
23. 2m 3 ⫹ 3m 2 ⫺ 18m ⫺ 27
18. p 2 ⫺ 132
m
no
ⴙ 3 m ⴚ 3 2m ⴙ 3
132 is not a perfect square. Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 156
156
Holt Algebra 1
1/3/06 6:15:20 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form C 7. Factor 21a 3 ⫹ 14a 2 ⫺ 9a ⫺ 6 by grouping.
1. Write the prime factorization of 1575.
Find the GCF. Factor each trinomial.
2. 420 and 1365
8. x 2 ⫹ 46x ⫹ 525
3. 102x 3 and 170x 2y 9. x 2 ⫺ 11x ⫹ 60
4. Jenny is displaying her photographs on a table at a sidewalk art show. She has 45 photos of people, 18 photos of landscapes, and 63 photos of pets. Each row will have the same number of photos, but people, landscapes, and pets will not appear in the same row. If she puts the greatest possible number of photos in each row, how many rows will there be?
10. x 2 ⫺ 11x ⫺ 126
11. Find an integer value of b that makes x 2 ⫹ bx ⫺ 81 factorable, and then factor the trinomial. b⫽
Factor. 12. Write the polynomial modeled by this geometric diagram and then factor.
5. ⫺8y 3 ⫹ 12y 2 ⫺ 6
6. 5n 3n ⫺ 4 ⫺ 2 4 ⫺ 3n
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 157
157
X
X
X
Holt Algebra 1
1/3/06 6:15:20 PM Process Black
Name CHAPTER
8
Date
Class
Chapter Test Form C
continued 19. 64x 6 ⫺ y 2
Factor each trinomial. 13. 45x 2 ⫹ 42x ⫹ 8
14. 28a 2 ⫹ 11a ⫺ 30
20. The area of a square in square feet is represented by 625z 2 ⫺ 150z ⫹ 9. Find an expression for the perimeter of the square. Then find the perimeter when z ⫽ 15 ft.
15. Determine whether each value of c makes 10x 2 ⫹ 19x ⫹ c factorable. If so, factor it.
expression: perimeter when z ⫽ 15 ft:
c ⫽ ⫺15
21. Tell whether 3x 2x 2 ⫹ 3x ⫺ 30 is completely factored. If not, factor it.
c ⫽ ⫺9 c ⫽ ⫺2 Determine whether the trinomial is a perfect square. If so, factor it. If not, explain why. 16. 81n 2 ⫹ 90n ⫹ 100
Factor each polynomial completely. 22. 36x 4 ⫹ 72x 3 ⫹ 32x 2
17. 49x 2 ⫺ 182x ⫹ 169 23. 36m 3 ⫹ 9m 2 ⫺ 4m ⫺ 1
Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why. 18. 121p 2 ⫺ 40
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107c08_Assess.indd 158
158
Holt Algebra 1
1/3/06 6:15:21 PM Process Black
Answer Key
continued
4. G
4. A
5. D
5. D
6. J
6. A
7. B
7. A
8. H
8. B
9. C
9. B
10. H
10. D
11. B
11. B
12. G
12. B
13. B
13. B
14. F
14. B
15. B
15. A
16. G
16. A
Section Quiz: Lessons 8-5 to 8-6
17. D
1. A
18. B
2. J
19. B
3. B
20. D
4. F
21. A
5. A
22. B
6. H
23. B
7. C
Chapter Test Form B
8. G
1. B
9. C
2. G
10. F
3. C
11. C
4. H
12. F
5. D
13. C
6. H
14. H
7. A 8. G
Chapter Test Form A
9. D
1. A 2. C 3. A
10. H 11. D 12. H
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107_Assess_Answer.indd 279
279
Holt Algebra 1
1/4/06 12:18:22 PM
Answer Key
continued
13. C
22. J
14. H
23. C
15. D
Chapter Test Form A
16. J
2 2 1 2 3
17. B
2. 4
18. G
3. 6x
19. D
4. 11 pages
2
20. J
2 5. 10y 3y 5
21. B
6. n 3 n 8
22. H
2 7. a 5 a 2
23. D
8. x 3 x 7
Chapter Test Form C
9. x 5 x 2
1. A
10. cannot be factored
2. H
11. 14, 2, 2, or 14 x 1 x 15 , x 3 x 5 , x 3 x 5 , or x 1 x 15
3. C 4. H 5. C 6. J 7. A 8. H 9. C 10. J 11. A 12. J 13. C 14. G 15. B 16. G 17. D
12. x 2 12x 20 x 2 x 10 13. 7x 1 x 4 14. a 1 3a 7 15. cannot be factored; 3x 1 x 2 16. no; 50n 2 n 5 2 17. yes; x 9
18. no; 30 is not a perfect square. 19. yes; x 10 x 10 20. 4z 24; 40 ft 21. no; 4 8x 5 x 3 22. 5x x 10 x 2 23. 3 m 4 m 2 m 2 2
Chapter Test Form B 4 1. 2 11
18. H
2. 18
19. D
3. 6x
20. J
4. 11 rows
21. D Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107_Assess_Answer.indd 280
2
280
Holt Algebra 1
1/4/06 12:18:23 PM
Answer Key
continued
5. 2y 7y 2 14y 27
12. 14x 2 57x 45 14x 15 x 3
6. cannot be factored
13. 3x 2 15x 4
7. 3a 4 5a 2
14. 4a 5 7a 6
8. x 6 x 3
15. 2x 5 5x 3 ; cannot be factored; x 2 10x 1
2
9. x 3 x 10 10. x 5 x 10
16. no; 90n 2 9n 10
11. 43, x 1 x 42 ; 23, b 2 b 21 ; 17, b 3 b 14 ; 13, b 6 b 7
2 17. yes; 7x 13
12. 18x 2 21x 5 3x 1 6x 5
18. no; 40 is not a perfect square. 3 3 19. yes; 8x y 8x y
13. x 4 3x 35
20. 100z 12; 1488 ft
14. 3a 5 9a 1
21. yes; completely factored
15. x 5 5x 3 ; cannot be factored; x 4 5x 2 16. no; 72n 2 n 6 2 17. yes; 3x 5
2 22. 4x 3x 2 3x 4
23. 3m 1 3m 1 4m 1 Performance Assessment 1. 4x 3 2x 1
18. no; 132 is not a perfect square.
2. 4 4x 3 2x 1
19. yes; 4x 7 4x 7
3. 2; if both dimensions were multiplied by the same number to get 4, each must have been multiplied by 2 because 2 2 4.
20. 8z 36; 44 ft 21. no; x x 4 4x 3 3 22. 2x x 8 2x 1
2 4. 2x 5 ; 2x 5
23. m 3 m 3 2m 3
2 5. 9 2x ⴚ 5
Chapter Test Form C
6. 3; the scale factor is the square root of the ratio of the GCFs.
2 2 1 3 5 7
2. 105 3. 34x
7. 2
2
8. 5
4. 14 rows 5. 2 4y 6y 3 3
2
6. 3n 4 5n 2
10,000 9. 400; 10,000; _______ 25; 25 5. 400 Cumulative Test
2 7. 3a 2 7a 3
1. A
8. x 21 x 25
2. H
9. cannot be factored
3. C
10. x 7 x 18
4. H
11. 80, 24, 0, 24, or 80 x 1 x 81 , x 3 x 27 , x 9 x 9 , x 3 x 27 , or x 1 x 81
5. A
Copyright © by Holt, Rinehart and Winston. All rights reserved.
a107_Assess_Answer.indd 281
6. H
281
Holt Algebra 1
6/2/06 2:13:08 PM
