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

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

1.Factor fully: −9x + 6

Answer: −3(3x − 2)

  1. Highest common factor: −3
  2. −9x + 6 = −3(3x − 2)
  3. Check by expanding the parentheses.
2.Factor fully: 6x2 − 36x − 48

Answer: 6(x2−6x−8)

  1. Highest common factor: 6
  2. 6x2 − 36x − 48 = 6(x2 − 6x − 8)
  3. Check by expanding the parentheses.
3.Factor fully: 25ab + 15a

Answer: 5a(5b + 3)

  1. Highest common factor: 5a
  2. 25ab + 15a = 5a(5b + 3)
  3. Check by expanding the parentheses.
4.Factor fully: −36x − 81

Answer: −9(4x + 9)

  1. Highest common factor: −9
  2. −36x − 81 = −9(4x + 9)
  3. Check by expanding the parentheses.
5.Factor fully: 4x2 + 16x − 36

Answer: 4(x2+4x−9)

  1. Highest common factor: 4
  2. 4x2 + 16x − 36 = 4(x2 + 4x − 9)
  3. Check by expanding the parentheses.
6.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.
7.Factor fully: −16x − 20

Answer: −4(4x + 5)

  1. Highest common factor: −4
  2. −16x − 20 = −4(4x + 5)
  3. Check by expanding the parentheses.
8.Factor fully: 15x2 + 15x + 10

Answer: 5(3x2+3x+2)

  1. Highest common factor: 5
  2. 15x2 + 15x + 10 = 5(3x2 + 3x + 2)
  3. Check by expanding the parentheses.
9.Factor fully: 20ab − 24a

Answer: 4a(5b − 6)

  1. Highest common factor: 4a
  2. 20ab − 24a = 4a(5b − 6)
  3. Check by expanding the parentheses.
10.Factor fully: −15x + 12

Answer: −3(5x − 4)

  1. Highest common factor: −3
  2. −15x + 12 = −3(5x − 4)
  3. Check by expanding the parentheses.
11.Factor fully: 16x2 − 8x + 20

Answer: 4(4x2−2x+5)

  1. Highest common factor: 4
  2. 16x2 − 8x + 20 = 4(4x2 − 2x + 5)
  3. Check by expanding the parentheses.
12.Factor fully: 20ab − 28a

Answer: 4a(5b − 7)

  1. Highest common factor: 4a
  2. 20ab − 28a = 4a(5b − 7)
  3. Check by expanding the parentheses.
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