8th Grade Factoring Expressions (Common Factors) Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the 8th Grade algebraic expressions worksheet.
Success TutoringWorksheetsAnswer sheet8th Grade · Mathematics · Algebraic Expressions8th Grade Factoring Expressions (Common Factors) Worksheet — Level 1 — Practice Set 4 — Answers
Find the highest common factor of the terms and write it outside the parentheses.
1.Factor fully: 24x + 42
Answer: 6(4x + 7)
- Highest common factor: 6
- 24x + 42 = 6(4x + 7)
- Check by expanding the parentheses.
2.Factor fully: 20x − 35
Answer: 5(4x − 7)
- Highest common factor: 5
- 20x − 35 = 5(4x − 7)
- Check by expanding the parentheses.
3.Factor fully: 18x − 42
Answer: 6(3x − 7)
- Highest common factor: 6
- 18x − 42 = 6(3x − 7)
- Check by expanding the parentheses.
4.Factor fully: 18x + 3
Answer: 3(6x + 1)
- Highest common factor: 3
- 18x + 3 = 3(6x + 1)
- Check by expanding the parentheses.
5.Factor fully: 42x + 7
Answer: 7(6x + 1)
- Highest common factor: 7
- 42x + 7 = 7(6x + 1)
- Check by expanding the parentheses.
6.Factor fully: 4x − 14
Answer: 2(2x − 7)
- Highest common factor: 2
- 4x − 14 = 2(2x − 7)
- Check by expanding the parentheses.
7.Factor fully: 40x − 56
Answer: 8(5x − 7)
- Highest common factor: 8
- 40x − 56 = 8(5x − 7)
- Check by expanding the parentheses.
8.Factor fully: 42x + 35
Answer: 7(6x + 5)
- Highest common factor: 7
- 42x + 35 = 7(6x + 5)
- Check by expanding the parentheses.
9.Factor fully: 9x − 3
Answer: 3(3x − 1)
- Highest common factor: 3
- 9x − 3 = 3(3x − 1)
- Check by expanding the parentheses.
10.Factor fully: 12x − 21
Answer: 3(4x − 7)
- Highest common factor: 3
- 12x − 21 = 3(4x − 7)
- Check by expanding the parentheses.
11.Factor fully: 12x − 6
Answer: 6(2x − 1)
- Highest common factor: 6
- 12x − 6 = 6(2x − 1)
- Check by expanding the parentheses.
12.Factor fully: 4x − 6
Answer: 2(2x − 3)
- Highest common factor: 2
- 4x − 6 = 2(2x − 3)
- Check by expanding the parentheses.
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.