Math worksheet for factoring algebraic expressions, featuring 30 problems to practice factoring linear expressions.

Let's solve the problem step by step.

We are asked to factor each expression. Factoring means writing an expression as a product of its factors, usually by finding the greatest common factor (GCF) of the terms and factoring it out.

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🔧 General Method:

For an expression like $ ax + b $, we look for the greatest common factor (GCF) of the coefficients and variables, then factor it out.

Example:
$ 3x + 15 $
- GCF of 3 and 15 is 3
- Factor out 3: $ 3(x + 5) $

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Now let’s go through all 30 problems:

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#### 1. $ 3x + 15 $
GCF = 3 → $ 3(x + 5) $

#### 2. $ 8y - 72 $
GCF = 8 → $ 8(y - 9) $

#### 3. $ 9a + 18 $
GCF = 9 → $ 9(a + 2) $

#### 4. $ 3b - 27 $
GCF = 3 → $ 3(b - 9) $

#### 5. $ 5c + 40 $
GCF = 5 → $ 5(c + 8) $

#### 6. $ 9a + 18 $
Same as #3 → $ 9(a + 2) $

#### 7. $ 6c + 18 $
GCF = 6 → $ 6(c + 3) $

#### 8. $ 8c - 8 $
GCF = 8 → $ 8(c - 1) $

#### 9. $ 5x - 10 $
GCF = 5 → $ 5(x - 2) $

#### 10. $ 2b - 16 $
GCF = 2 → $ 2(b - 8) $

#### 11. $ 8b + 72 $
GCF = 8 → $ 8(b + 9) $

#### 12. $ 7c - 35 $
GCF = 7 → $ 7(c - 5) $

#### 13. $ 5x - 15 $
GCF = 5 → $ 5(x - 3) $

#### 14. $ 6a - 48 $
GCF = 6 → $ 6(a - 8) $

#### 15. $ 3a - 6 $
GCF = 3 → $ 3(a - 2) $

#### 16. $ 9c - 63 $
GCF = 9 → $ 9(c - 7) $

#### 17. $ 3z + 9 $
GCF = 3 → $ 3(z + 3) $

#### 18. $ 6b - 12 $
GCF = 6 → $ 6(b - 2) $

#### 19. $ 2y + 18 $
GCF = 2 → $ 2(y + 9) $

#### 20. $ 3b - 6 $
GCF = 3 → $ 3(b - 2) $

#### 21. $ 3x + 24 $
GCF = 3 → $ 3(x + 8) $

#### 22. $ 9x - 18 $
GCF = 9 → $ 9(x - 2) $

#### 23. $ 2c + 16 $
GCF = 2 → $ 2(c + 8) $

#### 24. $ 7b - 28 $
GCF = 7 → $ 7(b - 4) $

#### 25. $ 7x - 56 $
GCF = 7 → $ 7(x - 8) $

#### 26. $ 8z - 56 $
GCF = 8 → $ 8(z - 7) $

#### 27. $ 7z - 28 $
GCF = 7 → $ 7(z - 4) $

#### 28. $ 9b + 27 $
GCF = 9 → $ 9(b + 3) $

#### 29. $ 4b + 24 $
GCF = 4 → $ 4(b + 6) $

#### 30. $ 6c + 36 $
GCF = 6 → $ 6(c + 6) $

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✔ Final Answer List:

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) $

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📌 Summary:

All expressions were factored by identifying the greatest common factor (GCF) of the terms and factoring it out. This is the basic method for factoring binomials with two terms.

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