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

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

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

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

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

1.Factorise fully: −14x + 49

Answer: −7(2x − 7)

  1. Highest common factor: −7
  2. −14x + 49 = −7(2x − 7)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 + 8x − 6

Answer: 2(2x2+4x−3)

  1. Highest common factor: 2
  2. 4x2 + 8x − 6 = 2(2x2 + 4x − 3)
  3. Check by expanding the brackets.
3.Factorise fully: 3ab − 15a

Answer: 3a(b − 5)

  1. Highest common factor: 3a
  2. 3ab − 15a = 3a(b − 5)
  3. Check by expanding the brackets.
4.Factorise fully: −7x − 49

Answer: −7(x + 7)

  1. Highest common factor: −7
  2. −7x − 49 = −7(x + 7)
  3. Check by expanding the brackets.
5.Factorise fully: 5x2 − 10x − 45

Answer: 5(x2−2x−9)

  1. Highest common factor: 5
  2. 5x2 − 10x − 45 = 5(x2 − 2x − 9)
  3. Check by expanding the brackets.
6.Factorise fully: 18ab − 24a

Answer: 6a(3b − 4)

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

Answer: −3(2x + 1)

  1. Highest common factor: −3
  2. −6x − 3 = −3(2x + 1)
  3. Check by expanding the brackets.
8.Factorise fully: 4x2 − 28x + 12

Answer: 4(x2−7x+3)

  1. Highest common factor: 4
  2. 4x2 − 28x + 12 = 4(x2 − 7x + 3)
  3. Check by expanding the brackets.
9.Factorise fully: 6ab − 24a

Answer: 6a(b − 4)

  1. Highest common factor: 6a
  2. 6ab − 24a = 6a(b − 4)
  3. Check by expanding the brackets.
10.Factorise fully: −18x + 42

Answer: −6(3x − 7)

  1. Highest common factor: −6
  2. −18x + 42 = −6(3x − 7)
  3. Check by expanding the brackets.
11.Factorise fully: 15x2 + 15x − 20

Answer: 5(3x2+3x−4)

  1. Highest common factor: 5
  2. 15x2 + 15x − 20 = 5(3x2 + 3x − 4)
  3. Check by expanding the brackets.
12.Factorise fully: 6ab − 4a

Answer: 2a(3b − 2)

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