Algebra Worksheets | Algebraic expressions, Factoring polynomials ... - Free Printable

Let's solve each of these factoring problems step by step. The goal is to factor out the greatest common factor (GCF) from each expression. This means we look for the largest number and variable that divide all terms in the expression.

---

Factoring Expressions (A) – Solutions

We'll go through each problem:

---

1. $ 9a - 18 $
- GCF of 9 and 18 is 9
- Factor: $ 9(a - 2) $

✔ Answer: $ 9(a - 2) $

---

2. $ 4a^2 - 16a $
- GCF of $ 4a^2 $ and $ 16a $ is 4a
- Factor: $ 4a(a - 4) $

✔ Answer: $ 4a(a - 4) $

---

3. $ 6b^2 + 12b $
- GCF of $ 6b^2 $ and $ 12b $ is 6b
- Factor: $ 6b(b + 2) $

✔ Answer: $ 6b(b + 2) $

---

4. $ 9b^2 + 27b $
- GCF of $ 9b^2 $ and $ 27b $ is 9b
- Factor: $ 9b(b + 3) $

✔ Answer: $ 9b(b + 3) $

---

5. $ 3b + 12 $
- GCF of 3 and 12 is 3
- Factor: $ 3(b + 4) $

✔ Answer: $ 3(b + 4) $

---

6. $ 4x^2 - 20x $
- GCF of $ 4x^2 $ and $ 20x $ is 4x
- Factor: $ 4x(x - 5) $

✔ Answer: $ 4x(x - 5) $

---

7. $ 7c^2 + 56c $
- GCF of $ 7c^2 $ and $ 56c $ is 7c
- Factor: $ 7c(c + 8) $

✔ Answer: $ 7c(c + 8) $

---

8. $ b^2 + b $
- GCF of $ b^2 $ and $ b $ is b
- Factor: $ b(b + 1) $

✔ Answer: $ b(b + 1) $

---

9. $ 8b - 48 $
- GCF of 8 and 48 is 8
- Factor: $ 8(b - 6) $

✔ Answer: $ 8(b - 6) $

---

10. $ 4x + 36 $
- GCF of 4 and 36 is 4
- Factor: $ 4(x + 9) $

✔ Answer: $ 4(x + 9) $

---

11. $ 2b^2 - 12b $
- GCF of $ 2b^2 $ and $ 12b $ is 2b
- Factor: $ 2b(b - 6) $

✔ Answer: $ 2b(b - 6) $

---

12. $ 2b^2 + 18b $
- GCF of $ 2b^2 $ and $ 18b $ is 2b
- Factor: $ 2b(b + 9) $

✔ Answer: $ 2b(b + 9) $

---

13. $ 6c - 30 $
- GCF of 6 and 30 is 6
- Factor: $ 6(c - 5) $

✔ Answer: $ 6(c - 5) $

---

14. $ 8b^2 + 32b $
- GCF of $ 8b^2 $ and $ 32b $ is 8b
- Factor: $ 8b(b + 4) $

✔ Answer: $ 8b(b + 4) $

---

15. $ 6b^2 - 6b $
- GCF of $ 6b^2 $ and $ 6b $ is 6b
- Factor: $ 6b(b - 1) $

✔ Answer: $ 6b(b - 1) $

---

16. $ 2a - 12 $
- GCF of 2 and 12 is 2
- Factor: $ 2(a - 6) $

✔ Answer: $ 2(a - 6) $

---

17. $ 6a^2 + 48a $
- GCF of $ 6a^2 $ and $ 48a $ is 6a
- Factor: $ 6a(a + 8) $

✔ Answer: $ 6a(a + 8) $

---

18. $ 8x - 32 $
- GCF of 8 and 32 is 8
- Factor: $ 8(x - 4) $

✔ Answer: $ 8(x - 4) $

---

19. $ 8a^2 - 72a $
- GCF of $ 8a^2 $ and $ 72a $ is 8a
- Factor: $ 8a(a - 9) $

✔ Answer: $ 8a(a - 9) $

---

20. $ a^2 - 2a $
- GCF of $ a^2 $ and $ 2a $ is a
- Factor: $ a(a - 2) $

✔ Answer: $ a(a - 2) $

---

21. $ 4y + 20 $
- GCF of 4 and 20 is 4
- Factor: $ 4(y + 5) $

✔ Answer: $ 4(y + 5) $

---

22. $ 7b + 49 $
- GCF of 7 and 49 is 7
- Factor: $ 7(b + 7) $

✔ Answer: $ 7(b + 7) $

---

23. $ a^2 + 5a $
- GCF of $ a^2 $ and $ 5a $ is a
- Factor: $ a(a + 5) $

✔ Answer: $ a(a + 5) $

---

24. $ 9z - 72 $
- GCF of 9 and 72 is 9
- Factor: $ 9(z - 8) $

✔ Answer: $ 9(z - 8) $

---

25. $ 4c + 4 $
- GCF of 4 and 4 is 4
- Factor: $ 4(c + 1) $

✔ Answer: $ 4(c + 1) $

---

26. $ 6a + 42 $
- GCF of 6 and 42 is 6
- Factor: $ 6(a + 7) $

✔ Answer: $ 6(a + 7) $

---

27. $ 9b^2 + 9b $
- GCF of $ 9b^2 $ and $ 9b $ is 9b
- Factor: $ 9b(b + 1) $

✔ Answer: $ 9b(b + 1) $

---

28. $ 5a - 30 $
- GCF of 5 and 30 is 5
- Factor: $ 5(a - 6) $

✔ Answer: $ 5(a - 6) $

---

29. $ 3a^2 + 27a $
- GCF of $ 3a^2 $ and $ 27a $ is 3a
- Factor: $ 3a(a + 9) $

✔ Answer: $ 3a(a + 9) $

---

30. $ c^2 - 5c $
- GCF of $ c^2 $ and $ 5c $ is c
- Factor: $ c(c - 5) $

✔ Answer: $ c(c - 5) $

---

✔ Final Answers Summary:

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

---

🔍 Explanation:

To factor an expression like $ ax + bx $, you identify the greatest common factor (GCF) of both terms. Then, factor it out and write the remaining expression inside parentheses.

For example:
- In $ 6b^2 + 12b $, both terms have a factor of $ 6b $. So:
$$
6b^2 + 12b = 6b(b + 2)
$$

This method works for any binomial where there’s a common factor.

Let me know if you'd like this turned into a printable worksheet or need help with more advanced factoring (like trinomials)!