Success TutoringWorksheets

Year 10 Factorising Expressions (Common Factors) Worksheet — Level 1 — Answers

Answer sheet with worked solutions for the Year 10 algebraic expressions worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Algebraic Expressions

Year 10 Factorising Expressions (Common Factors) Worksheet — Level 1 — Answers

Find the highest common factor of the terms and write it outside the brackets.

1.Factorise fully: 28x − 21

Answer: 7(4x − 3)

  1. Highest common factor: 7
  2. 28x − 21 = 7(4x − 3)
  3. Check by expanding the brackets.
2.Factorise fully: 40x + 64

Answer: 8(5x + 8)

  1. Highest common factor: 8
  2. 40x + 64 = 8(5x + 8)
  3. Check by expanding the brackets.
3.Factorise fully: 12x − 32

Answer: 4(3x − 8)

  1. Highest common factor: 4
  2. 12x − 32 = 4(3x − 8)
  3. Check by expanding the brackets.
4.Factorise fully: 9x + 12

Answer: 3(3x + 4)

  1. Highest common factor: 3
  2. 9x + 12 = 3(3x + 4)
  3. Check by expanding the brackets.
5.Factorise fully: 12x − 2

Answer: 2(6x − 1)

  1. Highest common factor: 2
  2. 12x − 2 = 2(6x − 1)
  3. Check by expanding the brackets.
6.Factorise fully: 12x + 21

Answer: 3(4x + 7)

  1. Highest common factor: 3
  2. 12x + 21 = 3(4x + 7)
  3. Check by expanding the brackets.
7.Factorise fully: 30x − 18

Answer: 6(5x − 3)

  1. Highest common factor: 6
  2. 30x − 18 = 6(5x − 3)
  3. Check by expanding the brackets.
8.Factorise fully: 30x − 36

Answer: 6(5x − 6)

  1. Highest common factor: 6
  2. 30x − 36 = 6(5x − 6)
  3. Check by expanding the brackets.
9.Factorise fully: 35x − 56

Answer: 7(5x − 8)

  1. Highest common factor: 7
  2. 35x − 56 = 7(5x − 8)
  3. Check by expanding the brackets.
10.Factorise fully: 4x + 20

Answer: 4(x + 5)

  1. Highest common factor: 4
  2. 4x + 20 = 4(x + 5)
  3. Check by expanding the brackets.
11.Factorise fully: 7x − 21

Answer: 7(x − 3)

  1. Highest common factor: 7
  2. 7x − 21 = 7(x − 3)
  3. Check by expanding the brackets.
12.Factorise fully: 8x − 72

Answer: 8(x − 9)

  1. Highest common factor: 8
  2. 8x − 72 = 8(x − 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: