This worksheet provides 30 practice problems for students to factor simple linear algebraic expressions.

To solve the problem of factoring each expression, we need to identify the greatest common factor (GCF) of the terms in each expression and then factor it out. Let's go through the first few expressions as examples, and then I'll provide a general explanation.

Example Solutions:

1. 3x + 15
- The GCF of 3x and 15 is 3.
- Factor out 3: \(3(x + 5)\).
- Answer: \(3(x + 5)\).

2. 8y - 72
- The GCF of 8y and 72 is 8.
- Factor out 8: \(8(y - 9)\).
- Answer: \(8(y - 9)\).

3. 9a + 18
- The GCF of 9a and 18 is 9.
- Factor out 9: \(9(a + 2)\).
- Answer: \(9(a + 2)\).

4. 3b - 27
- The GCF of 3b and 27 is 3.
- Factor out 3: \(3(b - 9)\).
- Answer: \(3(b - 9)\).

5. 5c + 40
- The GCF of 5c and 40 is 5.
- Factor out 5: \(5(c + 8)\).
- Answer: \(5(c + 8)\).

6. 9a + 18
- The GCF of 9a and 18 is 9.
- Factor out 9: \(9(a + 2)\).
- Answer: \(9(a + 2)\).

7. 6c + 18
- The GCF of 6c and 18 is 6.
- Factor out 6: \(6(c + 3)\).
- Answer: \(6(c + 3)\).

8. 8c - 8
- The GCF of 8c and 8 is 8.
- Factor out 8: \(8(c - 1)\).
- Answer: \(8(c - 1)\).

9. 5x - 10
- The GCF of 5x and 10 is 5.
- Factor out 5: \(5(x - 2)\).
- Answer: \(5(x - 2)\).

10. 2b - 16
- The GCF of 2b and 16 is 2.
- Factor out 2: \(2(b - 8)\).
- Answer: \(2(b - 8)\).

General Explanation:

To factor an expression:
1. Identify the GCF of all the terms in the expression.
2. Factor out the GCF by dividing each term by the GCF.
3. Write the expression as the product of the GCF and the remaining terms in parentheses.

Complete Solutions:

Here are the solutions for all the expressions:

1. \(3x + 15 = 3(x + 5)\)
2. \(8y - 72 = 8(y - 9)\)
3. \(9a + 18 = 9(a + 2)\)
4. \(3b - 27 = 3(b - 9)\)
5. \(5c + 40 = 5(c + 8)\)
6. \(9a + 18 = 9(a + 2)\)
7. \(6c + 18 = 6(c + 3)\)
8. \(8c - 8 = 8(c - 1)\)
9. \(5x - 10 = 5(x - 2)\)
10. \(2b - 16 = 2(b - 8)\)
11. \(8b + 72 = 8(b + 9)\)
12. \(7c - 35 = 7(c - 5)\)
13. \(5x - 15 = 5(x - 3)\)
14. \(6a - 48 = 6(a - 8)\)
15. \(3a - 6 = 3(a - 2)\)
16. \(9c - 63 = 9(c - 7)\)
17. \(3z + 9 = 3(z + 3)\)
18. \(6b - 12 = 6(b - 2)\)
19. \(2y + 18 = 2(y + 9)\)
20. \(3b - 6 = 3(b - 2)\)
21. \(3x + 24 = 3(x + 8)\)
22. \(9x - 18 = 9(x - 2)\)
23. \(2c + 16 = 2(c + 8)\)
24. \(7b - 28 = 7(b - 4)\)
25. \(7x - 56 = 7(x - 8)\)
26. \(8z - 56 = 8(z - 7)\)
27. \(7z - 28 = 7(z - 4)\)
28. \(9b + 27 = 9(b + 3)\)
29. \(4b + 24 = 4(b + 6)\)
30. \(6c + 36 = 6(c + 6)\)

Final Answer:

\[
\boxed{
\begin{aligned}
1. & \ 3(x + 5) \\
2. & \ 8(y - 9) \\
3. & \ 9(a + 2) \\
4. & \ 3(b - 9) \\
5. & \ 5(c + 8) \\
6. & \ 9(a + 2) \\
7. & \ 6(c + 3) \\
8. & \ 8(c - 1) \\
9. & \ 5(x - 2) \\
10. & \ 2(b - 8) \\
11. & \ 8(b + 9) \\
12. & \ 7(c - 5) \\
13. & \ 5(x - 3) \\
14. & \ 6(a - 8) \\
15. & \ 3(a - 2) \\
16. & \ 9(c - 7) \\
17. & \ 3(z + 3) \\
18. & \ 6(b - 2) \\
19. & \ 2(y + 9) \\
20. & \ 3(b - 2) \\
21. & \ 3(x + 8) \\
22. & \ 9(x - 2) \\
23. & \ 2(c + 8) \\
24. & \ 7(b - 4) \\
25. & \ 7(x - 8) \\
26. & \ 8(z - 7) \\
27. & \ 7(z - 4) \\
28. & \ 9(b + 3) \\
29. & \ 4(b + 6) \\
30. & \ 6(c + 6) \\
\end{aligned}
}
\]