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: −30x + 48

Answer: −6(5x − 8)

  1. Highest common factor: −6
  2. −30x + 48 = −6(5x − 8)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 − 16x + 4

Answer: 4(x2−4x+1)

  1. Highest common factor: 4
  2. 4x2 − 16x + 4 = 4(x2 − 4x + 1)
  3. Check by expanding the brackets.
3.Factorise fully: 25ab + 20a

Answer: 5a(5b + 4)

  1. Highest common factor: 5a
  2. 25ab + 20a = 5a(5b + 4)
  3. Check by expanding the brackets.
4.Factorise fully: −5x − 10

Answer: −5(x + 2)

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

Answer: 2(2x2+5x−6)

  1. Highest common factor: 2
  2. 4x2 + 10x − 12 = 2(2x2 + 5x − 6)
  3. Check by expanding the brackets.
6.Factorise fully: 5ab + 25a

Answer: 5a(b + 5)

  1. Highest common factor: 5a
  2. 5ab + 25a = 5a(b + 5)
  3. Check by expanding the brackets.
7.Factorise fully: −40x + 48

Answer: −8(5x − 6)

  1. Highest common factor: −8
  2. −40x + 48 = −8(5x − 6)
  3. Check by expanding the brackets.
8.Factorise fully: 15x2 − 10x + 25

Answer: 5(3x2−2x+5)

  1. Highest common factor: 5
  2. 15x2 − 10x + 25 = 5(3x2 − 2x + 5)
  3. Check by expanding the brackets.
9.Factorise fully: 6ab − 14a

Answer: 2a(3b − 7)

  1. Highest common factor: 2a
  2. 6ab − 14a = 2a(3b − 7)
  3. Check by expanding the brackets.
10.Factorise fully: −9x − 54

Answer: −9(x + 6)

  1. Highest common factor: −9
  2. −9x − 54 = −9(x + 6)
  3. Check by expanding the brackets.
11.Factorise fully: 15x2 + 25x + 5

Answer: 5(3x2+5x+1)

  1. Highest common factor: 5
  2. 15x2 + 25x + 5 = 5(3x2 + 5x + 1)
  3. Check by expanding the brackets.
12.Factorise fully: 12ab − 3a

Answer: 3a(4b − 1)

  1. Highest common factor: 3a
  2. 12ab − 3a = 3a(4b − 1)
  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: