Success TutoringWorksheets

Year 9 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 3 — Answers

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

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

Year 9 Factorising 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.Factorise fully: −14x + 63

Answer: −7(2x − 9)

  1. Highest common factor: −7
  2. −14x + 63 = −7(2x − 9)
  3. Check by expanding the brackets.
2.Factorise fully: 20x2 + 15x + 20

Answer: 5(4x2+3x+4)

  1. Highest common factor: 5
  2. 20x2 + 15x + 20 = 5(4x2 + 3x + 4)
  3. Check by expanding the brackets.
3.Factorise fully: 8ab + 20a

Answer: 4a(2b + 5)

  1. Highest common factor: 4a
  2. 8ab + 20a = 4a(2b + 5)
  3. Check by expanding the brackets.
4.Factorise fully: −10x + 12

Answer: −2(5x − 6)

  1. Highest common factor: −2
  2. −10x + 12 = −2(5x − 6)
  3. Check by expanding the brackets.
5.Factorise fully: 4x2 − 24x + 16

Answer: 4(x2−6x+4)

  1. Highest common factor: 4
  2. 4x2 − 24x + 16 = 4(x2 − 6x + 4)
  3. Check by expanding the brackets.
6.Factorise fully: 15ab + 18a

Answer: 3a(5b + 6)

  1. Highest common factor: 3a
  2. 15ab + 18a = 3a(5b + 6)
  3. Check by expanding the brackets.
7.Factorise fully: −4x + 18

Answer: −2(2x − 9)

  1. Highest common factor: −2
  2. −4x + 18 = −2(2x − 9)
  3. Check by expanding the brackets.
8.Factorise fully: 5x2 − 15x − 30

Answer: 5(x2−3x−6)

  1. Highest common factor: 5
  2. 5x2 − 15x − 30 = 5(x2 − 3x − 6)
  3. Check by expanding the brackets.
9.Factorise fully: 3ab + 27a

Answer: 3a(b + 9)

  1. Highest common factor: 3a
  2. 3ab + 27a = 3a(b + 9)
  3. Check by expanding the brackets.
10.Factorise fully: −24x + 8

Answer: −8(3x − 1)

  1. Highest common factor: −8
  2. −24x + 8 = −8(3x − 1)
  3. Check by expanding the brackets.
11.Factorise fully: 6x2 + 14x + 10

Answer: 2(3x2+7x+5)

  1. Highest common factor: 2
  2. 6x2 + 14x + 10 = 2(3x2 + 7x + 5)
  3. Check by expanding the brackets.
12.Factorise fully: 8ab + 18a

Answer: 2a(4b + 9)

  1. Highest common factor: 2a
  2. 8ab + 18a = 2a(4b + 9)
  3. Check by expanding the brackets.
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: