Factoring Non-Quadratic Expressions with No Squares, Simple ... - Free Printable

Let’s solve each problem one by one. We’re factoring expressions — that means we’re looking for the biggest number (or variable) that divides evenly into both terms, and then writing the expression as a product of that number and what’s left.

We’ll go through all 30 problems carefully.

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1. 3x + 15
Both 3 and 15 are divisible by 3.
→ 3(x + 5)

2. 8y - 72
8 and 72 → GCF is 8
→ 8(y - 9)

3. 9a + 18
9 and 18 → GCF is 9
→ 9(a + 2)

4. 3b - 27
3 and 27 → GCF is 3
→ 3(b - 9)

5. 5c + 40
5 and 40 → GCF is 5
→ 5(c + 8)

6. 9a + 18
Same as #3 → 9(a + 2)

7. 6c + 18
6 and 18 → GCF is 6
→ 6(c + 3)

8. 8c - 8
8 and 8 → GCF is 8
→ 8(c - 1)

9. 5x - 10
5 and 10 → GCF is 5
→ 5(x - 2)

10. 2b - 16
2 and 16 → GCF is 2
→ 2(b - 8)

11. 8b + 72
8 and 72 → GCF is 8
→ 8(b + 9)

12. 7c - 35
7 and 35 → GCF is 7
→ 7(c - 5)

13. 5x - 15
5 and 15 → GCF is 5
→ 5(x - 3)

14. 6a - 48
6 and 48 → GCF is 6
→ 6(a - 8)

15. 3a - 6
3 and 6 → GCF is 3
→ 3(a - 2)

16. 9c - 63
9 and 63 → GCF is 9
→ 9(c - 7)

17. 3z + 9
3 and 9 → GCF is 3
→ 3(z + 3)

18. 6b - 12
6 and 12 → GCF is 6
→ 6(b - 2)

19. 2y + 18
2 and 18 → GCF is 2
→ 2(y + 9)

20. 3b - 6
3 and 6 → GCF is 3
→ 3(b - 2)

21. 3x + 24
3 and 24 → GCF is 3
→ 3(x + 8)

22. 9x - 18
9 and 18 → GCF is 9
→ 9(x - 2)

23. 2c + 16
2 and 16 → GCF is 2
→ 2(c + 8)

24. 7b - 28
7 and 28 → GCF is 7
→ 7(b - 4)

25. 7x - 56
7 and 56 → GCF is 7
→ 7(x - 8)

26. 8z - 56
8 and 56 → GCF is 8
→ 8(z - 7)

27. 7z - 28
7 and 28 → GCF is 7
→ 7(z - 4)

28. 9b + 27
9 and 27 → GCF is 9
→ 9(b + 3)

29. 4b + 24
4 and 24 → GCF is 4
→ 4(b + 6)

30. 6c + 36
6 and 36 → GCF is 6
→ 6(c + 6)

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