Ch · Web viewHolt McDougal Algebra 1 Title Ch Author laserwords Last modified by Oberman, Alvin Created Date 5/13/2014 2:15:00 PM Company PMG Other titles Ch

Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form A

Select the best answer.1. Which is the prime factorization of 24?

A 2 • 2 • 2 • 3B 4 • 6

2. Find the GCF of 12 and 30.A 2 C 6B 3 D 36

3. Find the GCF of 5x

3 and 15x.A 5x C 15xB 5x

3 D 15x

3

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 8B 14

5. Factor 16y

2 12y completely.A y(16y 12)B 2y(8y 6)C 4(4y

2 3y)D 4y(4y 3)

6. Factor n(n 2) 7(n 2).A (n 2) (n 7)B 2(n 2) (n 7)

7. Factor a

2 3a 8a 24 by grouping.A (a 3) (a 8)B (a2 3a) (8a 24)C 8a(a 3)D cannot be factored

8. Factor x

2 12x 35.A (x 1) (x 35)B (x 5) (x 7)

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

10. Factor x


11. Which value of b would makex

2 bx 16 factorable?A 10B 6

12. Write the factored form of the polynomial that is modeled by this geometric diagram.

x

2 4x

2x 8

A (x 1) (x 8)B (x 2) (x 4)C (x

2 4x) (2x 8)D (2x 8) (4x 8)

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form A continued

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

15. Which value of c would NOT make 2x

2 5x c factorable?A 2B 3

16. Determine whether n

2 20n 100 is a perfect square trinomial.

A yesB no

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

18. Determine whether p

2 40 is a difference of two squares.

A yesB no

19. Determine whether x

2 16 is a difference of two squares. If so, choose the correct factorization.

A yes; (x 4)

2

B yes; (x 4) (x 4)C yes; (x 4)

2

D no20. The area of a square is represented by

z

2 10z 25. Which expression represents the perimeter of the square?

A z 5B z 9C 2z 10D 4z 20

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.

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



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form B


A 2 • 2 • 2 • 15 C 3 • 5 • 8B 2 • 2 • 2 • 3 • 5 D 10 • 12

2. Find the GCF of 42 and 70.F 7 H 196G 14 J 210


2 and 45x

5.A 5x

2 C 15x

2

B 5x

5 D 15x

5

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 19G 15 J 38

5. Factor 30y

3 6y

2 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)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

7. Factor 6a3 3a2 8a 4 by grouping.A (2a 1) (3a2 4)B (2a 4) (3a2 1)C (6a3 3a2) (8a 4)D cannot be factored

8. Factor x

2 8x 12.F (x 1) (x 12)G (x 2) (x 6)H (x 3) (x 4)J cannot be factored

9. Factor x


10. Factor x



2 bx 30 factorable?A 31 C 11B 17 D 13


12x

2 9x

4x 3

F (x 3) (12x 1)G (2x 3) (6x 1)H (3x 1) (4x 3)J (12x

2 4x) (9x 3)



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form B continued

13. Factor 5x

2 39x 54.A (x 2) (5x 27)B (x 3) (5x 18)C (x 6) (5x 9)D cannot be factored

14. Factor 8a2 10a 7.F (2a 7) (4a 1)G (2a 1) (4a 7)H (2a 1) (4a 7)J cannot be factored


2 5x c factorable?A 22 C 2B 2 D 22

16. Determine whether n

2 10n 25 is a perfect square trinomial. If so, choose the correct factorization.

F yes; (n 5)

2

G yes; (n 5)

2

H yes; (n 5) (n 5)J no

17. Determine whether 16x


A yes; (4x 3)

2

B yes; (4x 3)

2

C yes; (4x 3) (4x 3)D no

18. Determine whether p2 36 is a difference of two squares. If so, choose the correct factorization.

F yes; (p 6)

2

G yes; (p 6) (p 6)H yes; (p 18) (p 18)J no



A yes; (2x 5)

2

B yes; (2x 5) (2x 5)C yes; (2x 10) (2x 10)D no

20. The area of a square is represented by 9z


F 3z 2 H 6z 4G 3z 2 J 12z 8

21. Is x(4x

2 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.

C no; the trinomial 4x

2 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.

22. Completely factor 3x

4 15x

3 18x

2.F x

2(3x 2) (1x 9)G 3(x

2 1) (x

2 6)H 3x

2(x 1) (x 6)J cannot be factored

23. Completely factor3m

3 5m

2 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)



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form C


A 2

3 • 3 • 5 • 17 C 8 • 15 • 17B 2

3 • 5 • 51 D 40 • 512. Find the GCF of 330 and 2100.

F 3 H 30G 5 J 60


2 and 105y

2.A 5 C 15B 5x

2y

2 D 15x

2y

2

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 15G 6 J 30

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)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

7. Factor 8a3 6a2 3 4a by grouping.A (2a2 1) (4a 3)B (2a2 1) (4a 3)C (1) (2a2 1) (4a 3)D cannot be factored

8. Factor x


9. Factor x


10. Factor x



2 bx 36 factorable?A 20 C 5B 9 D 35


8x

2 18x

12x 27

F (2x 9) (4x 3)G (x 9) (8x 3)H (x 3) (8x 9)J (2x 3) (4x 9)



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter 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

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


2 13x c factorable?A 5 C 2B 2 D 5

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



A yes; (3x 20)

2

B yes; (3x 20)

2

C yes; (3x 20) (3x 20)D no

18. Determine whether 9p


F yes; (3p 15)

2

G yes; (3p 15)

2

H yes; (3p 15) (3p 15)J no


2 25y

16 is a difference of two squares. If so, choose the correct factorization.

A yes; (7x 5y

4)

2

B yes; (7x 5y

4) (7x 5y

4)C yes; (7x 5y

8) (7x 5y

8)D no

20. The area of a square is represented by 81z


F 9z 17 H 18z 34G 9z 21 J 36z 68

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.

22. Completely factor 9x

4 15x

3 2.F 3x

2(3x

2 5x 2)G 3x

2(3x 2) (x 1)H (9x

2 1) (x

2 2)J cannot be factored

23. Completely factor4m

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)



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form A

1. Write the prime factorization of 36.

_________________________________________

Find the GCF.2. 8 and 28

_________________________________________

3. 6x

2 and 18x

5

_________________________________________

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?

_________________________________________

Factor.5. 30y

3 50y

_________________________________________

6. n(n 3) 8(n 3)

_________________________________________

7. Factor a

3 5a

2 2a 10 by grouping.

_________________________________________

Factor each trinomial.8. x

2 10x 21

_________________________________________

9. x

2 3x 10

_________________________________________

10. x

2 16x 55

_________________________________________

11. Find an integer value of b that makesx

2 bx 15 factorable, and then factor the trinomial.

b _________________________________________

_________________________________________

12. Write the polynomial modeled by this geometric diagram and then factor.

x

2 10x

2x 20_________________________________________



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form A continued

Factor each trinomial.13. 7x

2 29x 4

_________________________________________

14. 3a

2 4a 7_________________________________________

15. Determine whether each value of c makes 3x

2 7x c factorable. If so, factor it.

c 2 ___________________________________

c 2 ___________________________________

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__________________________________________________________________________________

Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why.18. p

2 30

__________________________________________________________________________________

19. x

2 100

_________________________________________

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.

expression: _____________________________

perimeter when z 4 ft: _________________

21. Tell whether (8x 5) (4x 12) is completely factored. If not, factor it._________________________________________

_________________________________________

_________________________________________

Factor each polynomial completely.22. 5x

3 40x

2 100x

_________________________________________

23. 3m

4 48

_________________________________________



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form B


_________________________________________


_________________________________________

3. 30x

2 and 66x

5

_________________________________________

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 ninth-graders 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?

_________________________________________

Factor.5. 14y

3 28y

2 54y

_________________________________________

6. n(2n 3) 4(2n 3)

_________________________________________

7. Factor 15a3 20a2 6a 8 by grouping.

_________________________________________


2 9x 18

_________________________________________

9. x

2 7x 30

_________________________________________

10. x

2 5x 50

_________________________________________



b _____________________________________

_________________________________________


18x

2 15x

6x 5

_________________________________________



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form B continued


2 47x 140

_________________________________________

14. 27a

2 42a 5

_________________________________________



c 15 _________________________________

c 4 ___________________________________

c 8 ___________________________________

Determine whether the trinomial is a perfect square. If so, factor it. If not, explain why.16. n

2 72n 36

__________________________________________________________________________________

17. 9x

2 30x 25

__________________________________________________________________________________

Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why.18. p

2 132

__________________________________________________________________________________

19. 16x

2 49

__________________________________________________________________________________

20. The area of a square in square feet is represented by 4z


expression: _____________________________

perimeter when z 10 ft: ________________

21. Tell whether x(4x

2 19x 12) is completely factored. If not, factor it.

_________________________________________

_________________________________________

_________________________________________


5 30x

4 16x

3

_________________________________________

23. 2m

3 3m

2 18m 27

_________________________________________



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form C


_________________________________________


_________________________________________

3. 102x

3 and 170x

2y

_________________________________________

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?

_________________________________________

Factor.5. 8y

3 12y

2 6

_________________________________________

6. 5n(3n 4) 2(4 3n)

_________________________________________

7. Factor 21a3 14a2 9a 6 by grouping.

_________________________________________


2 46x 525

_________________________________________

9. x

2 11x 60

_________________________________________

10. x

2 11x 126

_________________________________________



b _____________________________________

_________________________________________


14x

2 15x

42x 45

_________________________________________



Name_________________________________________ Date____________________ Class____________________

Factoring PolynomialsChapter Test Form C continued


2 42x 8

_________________________________________

14. 28a2 11a 30

_________________________________________



c 15 _________________________________

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

__________________________________________________________________________________

17. 49x

2 182x 169

__________________________________________________________________________________

Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why.18. 121p2 40

__________________________________________________________________________________

19. 64x

6 y

2

__________________________________________________________________________________

20. The area of a square in square feet is represented by 625z


expression: _____________________________

perimeter when z 15 ft: ________________

21. Tell whether 3x(2x

2 3x 30) is completely factored. If not, factor it.

__________________________________________________________________________________


4 72x

3 32x

2

_________________________________________

23. 36m

3 9m

2 4m 1

_________________________________________

Section A Quiz1. A 2. J3. B 4. G5. D 6. J

7. B 8. H9. C 10. H

11. B 12. G13. B 14. F15. B 16. G

Section B Quiz



Name_________________________________________ Date____________________ Class____________________

1. A 2. J3. B 4. F5. A 6. H7. C 8. G9. C 10. F

11. C 12. F13. C 14. H

Chapter Test Form A1. A 2. C3. A 4. A5. D 6. A7. A 8. B9. B 10. D

11. B 12. B13. B 14. B15. A 16. A17. D 18. B19. B 20. D21. A 22. B23. B

Chapter Test Form B1. B 2. G3. C 4. H5. D 6. H7. A 8. G9. D 10. H

11. D 12. H13. C 14. H15. D 16. J17. B 18. G19. D 20. J

21. B 22. H23. D

Chapter Test Form C1. A 2. H3. C 4. H5. C 6. J7. A 8. H9. C 10. J

11. A 12. J13. C 14. G15. B 16. G17. D 18. H19. D 20. J21. D 22. J23. C

Chapter Test Form A1 22 · 32 2. 4

3. 6x

2 4. 11 pages5. 10y(3y

2 5) 6. (n 3)(n 8)7. (a 5)(a2 2) 8. (x 3)(x 7)9. (x 5)(x 2)

10. cannot be factored11. 14, 2, 2, or 14; (x 1)(x 15),

(x 3)(x 5), (x 3)(x 5), or (x 1)(x 15)

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) 17. yes; (x 9)2

18. no; 30 is not a perfect square.19. yes; (x 10)(x 10)

Factoring PolynomialsAnswers continued

20. 4z 24; 40 ft21. no; 4(8x 5)(x 3)22. 5x(x 10)(x 2)

23. 3(m2 4)(m 2)(m 2)

Chapter Test Form B



Name_________________________________________ Date____________________ Class____________________

1. 24 · 11 2. 183. 6x

2 4. 11 rows5. 2y(7y

2 14y

2 27)6. cannot be factored7. (3a 4)(5a2 2) 8. (x 6)(x 3)9. (x 3)(x 10) 10. (x 5)(x 10)

11. 43, (x 1)(x 42); 23, (x 2)(x 21); 17, (x 3)( x 14); 13, (x 6)(x 7)

12. 18x

2 21x 5 (3x 1)(6x 5)13. (x 4)(3x 35) 14. (3a 5)(9a 1)15. (x 5)(5x 3); cannot be factored;

(x 4)(5x 2)16. no; 72n ≠ 2(n • 6) 17. yes; (3x 5)2

18. no; 132 is not a perfect square.19. yes; (4x 7)(4x 7)20. 8z 36; 44 ft

21. no; x(x 4)(4x 3)

22. 2x

3(x 8)(2x 1)

23. (m 3)(m 3)(2m 3)

Chapter Test Form C1 32 · 52 · 7 2. 105

3. 34x

2 4. 14 rows

5. 2(4y

3 6y

2 3) 6. (3n 4)(5n 2)

7. (3a 2)(7a

2 3) 8. (x 21)(x 25)

9. cannot be factored 10. (x 7)(x 18)

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)

12. 14x

2 57x 45 (14x 15)(x 3)

13. (3x 2)(15x 4) 14. (4a 5)(7a 6)

15. (2x 5)(5x 3); cannot be factored; (x 2)(10x 1)

16. no; 90n ≠ 2(9n · 10)17. yes; (7x 13)2

18. no; 40 is not a perfect square.19. yes; (8x

3 y)(8x

3 y)20. 100z 12; 1488 ft21. yes; completely factored

22. 4x

2(3x 2)(3x 4)23. (3m 1)(3m 1)(4m 1)

Chapter Performance Assessment1. (4x 3)(2x 1) 2. 4(4x 3)(2x 1)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.

4. (2x 5)2; 2x 55. 9(2x 5)2

6. 3; the scale factor is the square root of the ratio of the areas after the GCF has been divided out.

7. 2 8. 5

9. 400; 10,000; 25; 5.

Chapter Cumulative Test1. A 2. H3. C 4. H5. A 6. H7. B 8. J9. C 10. J

11. B 12. H13. D 14. H15. D 16. F17. B 18. J19. C 20. F21. C 22. F23. C 24. J



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Ch · Web viewHolt McDougal Algebra 1 Title Ch Author laserwords Last modified by Oberman, Alvin Created Date 5/13/2014 2:15:00 PM Company PMG Other titles Ch