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

Take out the highest common factor. Where the first term is negative, take out a negative factor.

1.Factor fully: −5x − 20

Answer: −5(x + 4)

  1. Highest common factor: −5
  2. −5x − 20 = −5(x + 4)
  3. Check by expanding the parentheses.
2.Factor fully: 6x2 − 24x + 12

Answer: 6(x2−4x+2)

  1. Highest common factor: 6
  2. 6x2 − 24x + 12 = 6(x2 − 4x + 2)
  3. Check by expanding the parentheses.
3.Factor fully: 24ab − 6a

Answer: 6a(4b − 1)

  1. Highest common factor: 6a
  2. 24ab − 6a = 6a(4b − 1)
  3. Check by expanding the parentheses.
4.Factor fully: −18x + 45

Answer: −9(2x − 5)

  1. Highest common factor: −9
  2. −18x + 45 = −9(2x − 5)
  3. Check by expanding the parentheses.
5.Factor fully: 24x2 − 18x − 18

Answer: 6(4x2−3x−3)

  1. Highest common factor: 6
  2. 24x2 − 18x − 18 = 6(4x2 − 3x − 3)
  3. Check by expanding the parentheses.
6.Factor fully: 3ab + 27a

Answer: 3a(b + 9)

  1. Highest common factor: 3a
  2. 3ab + 27a = 3a(b + 9)
  3. Check by expanding the parentheses.
7.Factor fully: −25x − 20

Answer: −5(5x + 4)

  1. Highest common factor: −5
  2. −25x − 20 = −5(5x + 4)
  3. Check by expanding the parentheses.
8.Factor fully: 4x2 + 20x − 28

Answer: 4(x2+5x−7)

  1. Highest common factor: 4
  2. 4x2 + 20x − 28 = 4(x2 + 5x − 7)
  3. Check by expanding the parentheses.
9.Factor fully: 10ab + 14a

Answer: 2a(5b + 7)

  1. Highest common factor: 2a
  2. 10ab + 14a = 2a(5b + 7)
  3. Check by expanding the parentheses.
10.Factor fully: −4x + 24

Answer: −4(x − 6)

  1. Highest common factor: −4
  2. −4x + 24 = −4(x − 6)
  3. Check by expanding the parentheses.
11.Factor fully: 4x2 − 28x − 4

Answer: 4(x2−7x−1)

  1. Highest common factor: 4
  2. 4x2 − 28x − 4 = 4(x2 − 7x − 1)
  3. Check by expanding the parentheses.
12.Factor fully: 3ab − 24a

Answer: 3a(b − 8)

  1. Highest common factor: 3a
  2. 3ab − 24a = 3a(b − 8)
  3. Check by expanding the parentheses.
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