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

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

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Success TutoringWorksheetsAnswer sheet8th Grade · Mathematics · Algebraic Expressions

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

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

1.Factor fully: 15a + 35b

Answer: 5(3a + 7b)

  1. Highest common factor: 5
  2. 15a + 35b = 5(3a + 7b)
  3. Check by expanding the parentheses.
2.Factor fully: 4x2 + 9x

Answer: x(4x + 9)

  1. Highest common factor: x
  2. 4x2 + 9x = x(4x + 9)
  3. Check by expanding the parentheses.
3.Factor fully: 24x − 6y

Answer: 6(4x − y)

  1. Highest common factor: 6
  2. 24x − 6y = 6(4x − y)
  3. Check by expanding the parentheses.
4.Factor fully: 2x2 + 10x

Answer: 2x(x + 5)

  1. Highest common factor: 2x
  2. 2x2 + 10x = 2x(x + 5)
  3. Check by expanding the parentheses.
5.Factor fully: 35a + 49b

Answer: 7(5a + 7b)

  1. Highest common factor: 7
  2. 35a + 49b = 7(5a + 7b)
  3. Check by expanding the parentheses.
6.Factor fully: 3x2 − 5x

Answer: x(3x − 5)

  1. Highest common factor: x
  2. 3x2 − 5x = x(3x − 5)
  3. Check by expanding the parentheses.
7.Factor fully: 54x − 45y

Answer: 9(6x − 5y)

  1. Highest common factor: 9
  2. 54x − 45y = 9(6x − 5y)
  3. Check by expanding the parentheses.
8.Factor fully: 24x2 − 20x

Answer: 4x(6x − 5)

  1. Highest common factor: 4x
  2. 24x2 − 20x = 4x(6x − 5)
  3. Check by expanding the parentheses.
9.Factor fully: 3x + 18y

Answer: 3(x + 6y)

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

Answer: 3x(5x − 6)

  1. Highest common factor: 3x
  2. 15x2 − 18x = 3x(5x − 6)
  3. Check by expanding the parentheses.
11.Factor fully: 5m − 40n

Answer: 5(m − 8n)

  1. Highest common factor: 5
  2. 5m − 40n = 5(m − 8n)
  3. Check by expanding the parentheses.
12.Factor fully: 30x2 + 42x

Answer: 6x(5x + 7)

  1. Highest common factor: 6x
  2. 30x2 + 42x = 6x(5x + 7)
  3. Check by expanding the parentheses.
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