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9th Grade Factoring Expressions (Common Factors) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the 9th Grade algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheet9th Grade · Mathematics · Algebraic Expressions

9th 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: 20a − 8b

Answer: 4(5a − 2b)

  1. Highest common factor: 4
  2. 20a − 8b = 4(5a − 2b)
  3. Check by expanding the parentheses.
2.Factor fully: 6x2 − 6x

Answer: 6x(x − 1)

  1. Highest common factor: 6x
  2. 6x2 − 6x = 6x(x − 1)
  3. Check by expanding the parentheses.
3.Factor fully: 45a − 81b

Answer: 9(5a − 9b)

  1. Highest common factor: 9
  2. 45a − 81b = 9(5a − 9b)
  3. Check by expanding the parentheses.
4.Factor fully: 15x2 + 27x

Answer: 3x(5x + 9)

  1. Highest common factor: 3x
  2. 15x2 + 27x = 3x(5x + 9)
  3. Check by expanding the parentheses.
5.Factor fully: 42m + 7n

Answer: 7(6m + n)

  1. Highest common factor: 7
  2. 42m + 7n = 7(6m + n)
  3. Check by expanding the parentheses.
6.Factor fully: 20x2 − 45x

Answer: 5x(4x − 9)

  1. Highest common factor: 5x
  2. 20x2 − 45x = 5x(4x − 9)
  3. Check by expanding the parentheses.
7.Factor fully: 21m + 49n

Answer: 7(3m + 7n)

  1. Highest common factor: 7
  2. 21m + 49n = 7(3m + 7n)
  3. Check by expanding the parentheses.
8.Factor fully: 4x2 − 10x

Answer: 2x(2x − 5)

  1. Highest common factor: 2x
  2. 4x2 − 10x = 2x(2x − 5)
  3. Check by expanding the parentheses.
9.Factor fully: 9a − 63b

Answer: 9(a − 7b)

  1. Highest common factor: 9
  2. 9a − 63b = 9(a − 7b)
  3. Check by expanding the parentheses.
10.Factor fully: 9x2 − 15x

Answer: 3x(3x − 5)

  1. Highest common factor: 3x
  2. 9x2 − 15x = 3x(3x − 5)
  3. Check by expanding the parentheses.
11.Factor fully: 40x + 8y

Answer: 8(5x + y)

  1. Highest common factor: 8
  2. 40x + 8y = 8(5x + y)
  3. Check by expanding the parentheses.
12.Factor fully: 16x2 + 36x

Answer: 4x(4x + 9)

  1. Highest common factor: 4x
  2. 16x2 + 36x = 4x(4x + 9)
  3. Check by expanding the parentheses.
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