Factoring expressions worksheet with 30 algebraic problems to factor.

To solve these problems, we need to factor each expression. Factoring means finding what number or variable is common to both parts of the expression and pulling it out front.

Here is how to do it step-by-step for any problem on this list:
1. Look at the two terms (the numbers/letters before and after the plus or minus sign).
2. Find the Greatest Common Factor (GCF). This is the biggest number that divides evenly into both numbers. If there are letters, check if they are in both terms too.
3. Write the GCF outside a set of parentheses.
4. Divide each original term by the GCF to find what goes inside the parentheses.

Let's work through the first few to see the pattern, then I will list the answers for all 30.

Example 1: $3x + 15$
* Both 3 and 15 can be divided by 3.
* Put 3 outside: $3(\dots)$
* $3x \div 3 = x$
* $15 \div 3 = 5$
* Answer: $3(x + 5)$

Example 2: $8y - 72$
* Both 8 and 72 can be divided by 8. ($8 \times 9 = 72$)
* Put 8 outside: $8(\dots)$
* $8y \div 8 = y$
* $-72 \div 8 = -9$
* Answer: $8(y - 9)$

Example 3: $9a + 18$
* Both 9 and 18 can be divided by 9.
* Answer: $9(a + 2)$

I have calculated the factors for all 30 expressions below by finding the greatest common divisor for the coefficients.

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. $6(c + 6)$