8th Grade Factoring Expressions (Common Factors) Worksheet — Level 1 — 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 — Answers
Find the highest common factor of the terms and write it outside the parentheses.
1.Factor fully: 45x + 63
Answer: 9(5x + 7)
- Highest common factor: 9
- 45x + 63 = 9(5x + 7)
- Check by expanding the parentheses.
2.Factor fully: 48x + 8
Answer: 8(6x + 1)
- Highest common factor: 8
- 48x + 8 = 8(6x + 1)
- Check by expanding the parentheses.
3.Factor fully: 2x + 16
Answer: 2(x + 8)
- Highest common factor: 2
- 2x + 16 = 2(x + 8)
- Check by expanding the parentheses.
4.Factor fully: 6x + 54
Answer: 6(x + 9)
- Highest common factor: 6
- 6x + 54 = 6(x + 9)
- Check by expanding the parentheses.
5.Factor fully: 8x − 56
Answer: 8(x − 7)
- Highest common factor: 8
- 8x − 56 = 8(x − 7)
- Check by expanding the parentheses.
6.Factor fully: 20x − 32
Answer: 4(5x − 8)
- Highest common factor: 4
- 20x − 32 = 4(5x − 8)
- Check by expanding the parentheses.
7.Factor fully: 27x − 63
Answer: 9(3x − 7)
- Highest common factor: 9
- 27x − 63 = 9(3x − 7)
- Check by expanding the parentheses.
8.Factor fully: 36x − 30
Answer: 6(6x − 5)
- Highest common factor: 6
- 36x − 30 = 6(6x − 5)
- Check by expanding the parentheses.
9.Factor fully: 8x − 8
Answer: 8(x − 1)
- Highest common factor: 8
- 8x − 8 = 8(x − 1)
- Check by expanding the parentheses.
10.Factor fully: 12x − 28
Answer: 4(3x − 7)
- Highest common factor: 4
- 12x − 28 = 4(3x − 7)
- Check by expanding the parentheses.
11.Factor fully: 30x + 25
Answer: 5(6x + 5)
- Highest common factor: 5
- 30x + 25 = 5(6x + 5)
- Check by expanding the parentheses.
12.Factor fully: 14x + 35
Answer: 7(2x + 5)
- Highest common factor: 7
- 14x + 35 = 7(2x + 5)
- 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.
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