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8th Grade Factoring Expressions (Common Factors) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the 8th Grade algebraic expressions worksheet.

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8th Grade Factoring Expressions (Common Factors) Worksheet — Level 2 — Practice Set 3 — Answers

Find the highest common factor of the terms and write it outside the parentheses.

1.Factor fully: 16m − 4n

Answer: 4(4m − n)

  1. Highest common factor: 4
  2. 16m − 4n = 4(4m − n)
  3. Check by expanding the parentheses.
2.Factor fully: 6x2 − 18x

Answer: 6x(x − 3)

  1. Highest common factor: 6x
  2. 6x2 − 18x = 6x(x − 3)
  3. Check by expanding the parentheses.
3.Factor fully: 15m − 21n

Answer: 3(5m − 7n)

  1. Highest common factor: 3
  2. 15m − 21n = 3(5m − 7n)
  3. Check by expanding the parentheses.
4.Factor fully: 16x2 + 12x

Answer: 4x(4x + 3)

  1. Highest common factor: 4x
  2. 16x2 + 12x = 4x(4x + 3)
  3. Check by expanding the parentheses.
5.Factor fully: 18a − 48b

Answer: 6(3a − 8b)

  1. Highest common factor: 6
  2. 18a − 48b = 6(3a − 8b)
  3. Check by expanding the parentheses.
6.Factor fully: 12x2 + 8x

Answer: 4x(3x + 2)

  1. Highest common factor: 4x
  2. 12x2 + 8x = 4x(3x + 2)
  3. Check by expanding the parentheses.
7.Factor fully: 27m − 36n

Answer: 9(3m − 4n)

  1. Highest common factor: 9
  2. 27m − 36n = 9(3m − 4n)
  3. Check by expanding the parentheses.
8.Factor fully: 10x2 − 4x

Answer: 2x(5x − 2)

  1. Highest common factor: 2x
  2. 10x2 − 4x = 2x(5x − 2)
  3. Check by expanding the parentheses.
9.Factor fully: 9m − 81n

Answer: 9(m − 9n)

  1. Highest common factor: 9
  2. 9m − 81n = 9(m − 9n)
  3. Check by expanding the parentheses.
10.Factor fully: 30x2 + 48x

Answer: 6x(5x + 8)

  1. Highest common factor: 6x
  2. 30x2 + 48x = 6x(5x + 8)
  3. Check by expanding the parentheses.
11.Factor fully: 42m + 49n

Answer: 7(6m + 7n)

  1. Highest common factor: 7
  2. 42m + 49n = 7(6m + 7n)
  3. Check by expanding the parentheses.
12.Factor fully: 10x2 − 15x

Answer: 5x(2x − 3)

  1. Highest common factor: 5x
  2. 10x2 − 15x = 5x(2x − 3)
  3. Check by expanding the parentheses.
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