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

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

1.Factor fully: −12x − 54

Answer: −6(2x + 9)

  1. Highest common factor: −6
  2. −12x − 54 = −6(2x + 9)
  3. Check by expanding the parentheses.
2.Factor fully: 20x2 − 20x − 45

Answer: 5(4x2−4x−9)

  1. Highest common factor: 5
  2. 20x2 − 20x − 45 = 5(4x2 − 4x − 9)
  3. Check by expanding the parentheses.
3.Factor fully: 15ab + 12a

Answer: 3a(5b + 4)

  1. Highest common factor: 3a
  2. 15ab + 12a = 3a(5b + 4)
  3. Check by expanding the parentheses.
4.Factor fully: −4x − 16

Answer: −4(x + 4)

  1. Highest common factor: −4
  2. −4x − 16 = −4(x + 4)
  3. Check by expanding the parentheses.
5.Factor fully: 4x2 + 28x − 12

Answer: 4(x2+7x−3)

  1. Highest common factor: 4
  2. 4x2 + 28x − 12 = 4(x2 + 7x − 3)
  3. Check by expanding the parentheses.
6.Factor fully: 6ab − 54a

Answer: 6a(b − 9)

  1. Highest common factor: 6a
  2. 6ab − 54a = 6a(b − 9)
  3. Check by expanding the parentheses.
7.Factor fully: −9x − 54

Answer: −9(x + 6)

  1. Highest common factor: −9
  2. −9x − 54 = −9(x + 6)
  3. Check by expanding the parentheses.
8.Factor fully: 4x2 + 16x + 24

Answer: 4(x2+4x+6)

  1. Highest common factor: 4
  2. 4x2 + 16x + 24 = 4(x2 + 4x + 6)
  3. Check by expanding the parentheses.
9.Factor fully: 30ab + 12a

Answer: 6a(5b + 2)

  1. Highest common factor: 6a
  2. 30ab + 12a = 6a(5b + 2)
  3. Check by expanding the parentheses.
10.Factor fully: −21x − 14

Answer: −7(3x + 2)

  1. Highest common factor: −7
  2. −21x − 14 = −7(3x + 2)
  3. Check by expanding the parentheses.
11.Factor fully: 9x2 − 3x − 3

Answer: 3(3x2−x−1)

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

Answer: 2a(2b − 1)

  1. Highest common factor: 2a
  2. 4ab − 2a = 2a(2b − 1)
  3. Check by expanding the parentheses.
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