Success TutoringWorksheets

9th Grade Factoring Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — Answers

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

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheet9th Grade · Mathematics · Algebraic Expressions

9th 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: −2x + 16

Answer: −2(x − 8)

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

Answer: 4(2x2+x+1)

  1. Highest common factor: 4
  2. 8x2 + 4x + 4 = 4(2x2 + x + 1)
  3. Check by expanding the parentheses.
3.Factor fully: 3ab + 18a

Answer: 3a(b + 6)

  1. Highest common factor: 3a
  2. 3ab + 18a = 3a(b + 6)
  3. Check by expanding the parentheses.
4.Factor fully: −35x − 28

Answer: −7(5x + 4)

  1. Highest common factor: −7
  2. −35x − 28 = −7(5x + 4)
  3. Check by expanding the parentheses.
5.Factor fully: 9x2 + 9x + 24

Answer: 3(3x2+3x+8)

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

Answer: 4a(6b + 1)

  1. Highest common factor: 4a
  2. 24ab + 4a = 4a(6b + 1)
  3. Check by expanding the parentheses.
7.Factor fully: −20x − 28

Answer: −4(5x + 7)

  1. Highest common factor: −4
  2. −20x − 28 = −4(5x + 7)
  3. Check by expanding the parentheses.
8.Factor fully: 15x2 + 5x + 35

Answer: 5(3x2+x+7)

  1. Highest common factor: 5
  2. 15x2 + 5x + 35 = 5(3x2 + x + 7)
  3. Check by expanding the parentheses.
9.Factor fully: 24ab + 28a

Answer: 4a(6b + 7)

  1. Highest common factor: 4a
  2. 24ab + 28a = 4a(6b + 7)
  3. Check by expanding the parentheses.
10.Factor fully: −45x − 81

Answer: −9(5x + 9)

  1. Highest common factor: −9
  2. −45x − 81 = −9(5x + 9)
  3. Check by expanding the parentheses.
11.Factor fully: 10x2 + 25x + 45

Answer: 5(2x2+5x+9)

  1. Highest common factor: 5
  2. 10x2 + 25x + 45 = 5(2x2 + 5x + 9)
  3. Check by expanding the parentheses.
12.Factor fully: 12ab − 3a

Answer: 3a(4b − 1)

  1. Highest common factor: 3a
  2. 12ab − 3a = 3a(4b − 1)
  3. Check by expanding the parentheses.
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: