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Year 9 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — Answers

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

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Year 9 Factorising 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.Factorise fully: −2x − 16

Answer: −2(x + 8)

  1. Highest common factor: −2
  2. −2x − 16 = −2(x + 8)
  3. Check by expanding the brackets.
2.Factorise fully: 10x2 + 30x − 45

Answer: 5(2x2+6x−9)

  1. Highest common factor: 5
  2. 10x2 + 30x − 45 = 5(2x2 + 6x − 9)
  3. Check by expanding the brackets.
3.Factorise fully: 4ab − 6a

Answer: 2a(2b − 3)

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

Answer: −8(2x + 3)

  1. Highest common factor: −8
  2. −16x − 24 = −8(2x + 3)
  3. Check by expanding the brackets.
5.Factorise fully: 6x2 − 36x + 24

Answer: 6(x2−6x+4)

  1. Highest common factor: 6
  2. 6x2 − 36x + 24 = 6(x2 − 6x + 4)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab − 32a

Answer: 4a(3b − 8)

  1. Highest common factor: 4a
  2. 12ab − 32a = 4a(3b − 8)
  3. Check by expanding the brackets.
7.Factorise fully: −36x − 42

Answer: −6(6x + 7)

  1. Highest common factor: −6
  2. −36x − 42 = −6(6x + 7)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 + 12x − 2

Answer: 2(3x2+6x−1)

  1. Highest common factor: 2
  2. 6x2 + 12x − 2 = 2(3x2 + 6x − 1)
  3. Check by expanding the brackets.
9.Factorise fully: 4ab + 14a

Answer: 2a(2b + 7)

  1. Highest common factor: 2a
  2. 4ab + 14a = 2a(2b + 7)
  3. Check by expanding the brackets.
10.Factorise fully: −20x − 16

Answer: −4(5x + 4)

  1. Highest common factor: −4
  2. −20x − 16 = −4(5x + 4)
  3. Check by expanding the brackets.
11.Factorise fully: 4x2 − 10x − 10

Answer: 2(2x2−5x−5)

  1. Highest common factor: 2
  2. 4x2 − 10x − 10 = 2(2x2 − 5x − 5)
  3. Check by expanding the brackets.
12.Factorise fully: 9ab + 21a

Answer: 3a(3b + 7)

  1. Highest common factor: 3a
  2. 9ab + 21a = 3a(3b + 7)
  3. Check by expanding the brackets.
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