Factoring Non-Quadratic Expressions with Some Squares, Compound ... - Free Printable

I'll solve each factoring problem step by step, finding the greatest common factor (GCF) for each expression.

Let me work through all 30 problems:

1. 32x² + 8x
- GCF of 32 and 8 is 8
- Both terms have x
- Factor out 8x: 8x(4x + 1)

2. 32c - 24
- GCF of 32 and 24 is 8
- Factor out 8: 8(4c - 3)

3. 48b + 30
- GCF of 48 and 30 is 6
- Factor out 6: 6(8b + 5)

4. 6x + 12
- GCF of 6 and 12 is 6
- Factor out 6: 6(x + 2)

5. 56c + 8
- GCF of 56 and 8 is 8
- Factor out 8: 8(7c + 1)

6. 18z² - 30z
- GCF of 18 and 30 is 6
- Both terms have z
- Factor out 6z: 6z(3z - 5)

7. 72a - 64
- GCF of 72 and 64 is 8
- Factor out 8: 8(9a - 8)

8. 81b - 45
- GCF of 81 and 45 is 9
- Factor out 9: 9(9b - 5)

9. 7b² - 14b
- GCF of 7 and 14 is 7
- Both terms have b
- Factor out 7b: 7b(b - 2)

10. 35c - 40
- GCF of 35 and 40 is 5
- Factor out 5: 5(7c - 8)

11. 24y² - 42y
- GCF of 24 and 42 is 6
- Both terms have y
- Factor out 6y: 6y(4y - 7)

12. 14x² - 8x
- GCF of 14 and 8 is 2
- Both terms have x
- Factor out 2x: 2x(7x - 4)

13. 7a² - 5a
- No common numerical factor (7 and 5)
- Both terms have a
- Factor out a: a(7a - 5)

14. 30b + 10
- GCF of 30 and 10 is 10
- Factor out 10: 10(3b + 1)

15. 8z² + 6z
- GCF of 8 and 6 is 2
- Both terms have z
- Factor out 2z: 2z(4z + 3)

16. 15y² - 15y
- GCF of 15 and 15 is 15
- Both terms have y
- Factor out 15y: 15y(y - 1)

17. 8c² - 6c
- GCF of 8 and 6 is 2
- Both terms have c
- Factor out 2c: 2c(4c - 3)

18. 4z² + 12z
- GCF of 4 and 12 is 4
- Both terms have z
- Factor out 4z: 4z(z + 3)

19. 8y - 14
- GCF of 8 and 14 is 2
- Factor out 2: 2(4y - 7)

20. 16x² - 16x
- GCF of 16 and 16 is 16
- Both terms have x
- Factor out 16x: 16x(x - 1)

21. 18x - 6
- GCF of 18 and 6 is 6
- Factor out 6: 6(3x - 1)

22. 24y² + 42y
- GCF of 24 and 42 is 6
- Both terms have y
- Factor out 6y: 6y(4y + 7)

23. 14c² + 28c
- GCF of 14 and 28 is 14
- Both terms have c
- Factor out 14c: 14c(c + 2)

24. 7c² + 2c
- No common numerical factor (7 and 2)
- Both terms have c
- Factor out c: c(7c + 2)

25. 63c² + 14c
- GCF of 63 and 14 is 7
- Both terms have c
- Factor out 7c: 7c(9c + 2)

26. 8y² - 7y
- No common numerical factor (8 and 7)
- Both terms have y
- Factor out y: y(8y - 7)

27. 56c + 49
- GCF of 56 and 49 is 7
- Factor out 7: 7(8c + 7)

28. 12a - 12
- GCF of 12 and 12 is 12
- Factor out 12: 12(a - 1)

29. 24y + 16
- GCF of 24 and 16 is 8
- Factor out 8: 8(3y + 2)

30. 12c² + 20c
- GCF of 12 and 20 is 4
- Both terms have c
- Factor out 4c: 4c(3c + 5)

Final Answer:
1. 8x(4x + 1)
2. 8(4c - 3)
3. 6(8b + 5)
4. 6(x + 2)
5. 8(7c + 1)
6. 6z(3z - 5)
7. 8(9a - 8)
8. 9(9b - 5)
9. 7b(b - 2)
10. 5(7c - 8)
11. 6y(4y - 7)
12. 2x(7x - 4)
13. a(7a - 5)
14. 10(3b + 1)
15. 2z(4z + 3)
16. 15y(y - 1)
17. 2c(4c - 3)
18. 4z(z + 3)
19. 2(4y - 7)
20. 16x(x - 1)
21. 6(3x - 1)
22. 6y(4y + 7)
23. 14c(c + 2)
24. c(7c + 2)
25. 7c(9c + 2)
26. y(8y - 7)
27. 7(8c + 7)
28. 12(a - 1)
29. 8(3y + 2)
30. 4c(3c + 5)