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Algebra II worksheet

Using Prime Factorization

Find the prime factorization of each integer.

1. 84

 

2. 360

 

3. 616

 

4. 133

 

5. 2925

 

Find (a) the GCF and (b) the LCM of the following integers.

6. 30, 55

 

7. -66, 110

 

8. 245, -385

 

9. 2, 5, 13

 

10. 6, 10, 14

 

11. 36, 40, 90

 

Find (a) the GCF and (b) the LCM of the following monomials.

12. 12xy, 15xy²

 

13. -55mn³, 85m²n²

 

14. 42xy, -70yz

 

15. 108pqr², 144p²qr²

 

16. 10rs, 12rst, 14r²st²

Worksheet 4.5 Factoring Polynomials

Factor each polynomial.

1. y² + y

 

2. 8a^4 – 14a²b

 

3. 10x^8 + 15x^7 – 35x^5

 

4. 11a³b – 22a²b² + 55ab³

 

5. x² + 10x + 25

 

6. 4y² – 12y + 9

 

7. x² – 16

 

8. 4k² – 25

 

9. 25x² + 20xy + 4y²

 

10. 81p² – 49q²

 

11. 3x² + 12x + 12

 

12. 5c³ + 30c²d + 45cd²

 

13. rt² – r

 

14. 4x²y – 36y

 

15. 16n^4 – 1

 

16. x³ + 1

 

17. 64 – a³

 

18. t³ + 125

 

19. a(b + 2) – 3(b + 2)

 

20. m(n – 2) – (2 – n)

 

21. 20a³ – 5a² + 8a – 2

 

22. 10y³ + 10y² + 3y + 3

 

23. 5x²y – 7x² – 7 + 5y

Answer Key

4.4

1. 2² · 3 · 7

2. 2³ · 3² · 5

3. 2³ · 7 · 11

4. 7 · 19

5. 3² · 5² · 13

6. a. 5 b. 330

7. a. 22 b. 330

8. a. 35 b. 2695

9. a. 1 b. 130

10. a. 2 b. 210

11. a. 2. b. 360

12. a. 3xy b. 60xy²

13. a. 5mn² b. 935m²n³

14. 14y b. 210xyz

15. 36pqr² b. 432p²qr²

16. a. 2rs b. 420r²st²

4.5

1. y(y + 1)

2. 2a²(4a² – 7b)

3. 5x^5(2x³ + 3x² – 7)

4. 11ab(a² – 2ab + 5b²)

5. (x + 5) ²

6. (2y – 3) ²

7. (x + 4)(x – 4)

8. (2k + 5)(2k – 5)

9. (5x + 2y) ²

10. (9p + 7q)(9p – 7q)

11. 3(x + 2) ²

12. 5c(c + 3d) ²

13. r(t + 1)(t – 1)

14. 4y(x + 3)(x – 3)

15. (4n² + 1)(2n + 1)(2n – 1)

16. (x + 1)(x² – x + 1)

17. (4 – a)(16 + 4a + a²)

18. (t + 5)(t² – 5t + 25)

19. (a – 3)(b + 2)

20. (m + 1)(n – 2)

21. (5a² + 2)(4a – 1)

22. (10y² + 3)(y + 1)

23. (x² + 1)(5y – 7)

 

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