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8th Grade Factoring Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.Factor fully: −28x − 35

Answer: −7(4x + 5)

  1. Highest common factor: −7
  2. −28x − 35 = −7(4x + 5)
  3. Check by expanding the parentheses.
2.Factor fully: 2x2 − 8x − 4

Answer: 2(x2−4x−2)

  1. Highest common factor: 2
  2. 2x2 − 8x − 4 = 2(x2 − 4x − 2)
  3. Check by expanding the parentheses.
3.Factor fully: 5ab + 45a

Answer: 5a(b + 9)

  1. Highest common factor: 5a
  2. 5ab + 45a = 5a(b + 9)
  3. Check by expanding the parentheses.
4.Factor fully: −16x − 28

Answer: −4(4x + 7)

  1. Highest common factor: −4
  2. −16x − 28 = −4(4x + 7)
  3. Check by expanding the parentheses.
5.Factor fully: 4x2 − 2x + 12

Answer: 2(2x2−x+6)

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

Answer: 4a(b − 1)

  1. Highest common factor: 4a
  2. 4ab − 4a = 4a(b − 1)
  3. Check by expanding the parentheses.
7.Factor fully: −36x − 63

Answer: −9(4x + 7)

  1. Highest common factor: −9
  2. −36x − 63 = −9(4x + 7)
  3. Check by expanding the parentheses.
8.Factor fully: 12x2 − 21x − 18

Answer: 3(4x2−7x−6)

  1. Highest common factor: 3
  2. 12x2 − 21x − 18 = 3(4x2 − 7x − 6)
  3. Check by expanding the parentheses.
9.Factor fully: 6ab + 12a

Answer: 6a(b + 2)

  1. Highest common factor: 6a
  2. 6ab + 12a = 6a(b + 2)
  3. Check by expanding the parentheses.
10.Factor fully: −2x − 8

Answer: −2(x + 4)

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

Answer: 4(3x2−5x−4)

  1. Highest common factor: 4
  2. 12x2 − 20x − 16 = 4(3x2 − 5x − 4)
  3. Check by expanding the parentheses.
12.Factor fully: 24ab − 20a

Answer: 4a(6b − 5)

  1. Highest common factor: 4a
  2. 24ab − 20a = 4a(6b − 5)
  3. Check by expanding the parentheses.
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