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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: −28x − 63

Answer: −7(4x + 9)

  1. Highest common factor: −7
  2. −28x − 63 = −7(4x + 9)
  3. Check by expanding the brackets.
2.Factorise fully: 3x2 − 21x + 15

Answer: 3(x2−7x+5)

  1. Highest common factor: 3
  2. 3x2 − 21x + 15 = 3(x2 − 7x + 5)
  3. Check by expanding the brackets.
3.Factorise fully: 9ab + 3a

Answer: 3a(3b + 1)

  1. Highest common factor: 3a
  2. 9ab + 3a = 3a(3b + 1)
  3. Check by expanding the brackets.
4.Factorise fully: −15x − 40

Answer: −5(3x + 8)

  1. Highest common factor: −5
  2. −15x − 40 = −5(3x + 8)
  3. Check by expanding the brackets.
5.Factorise fully: 12x2 + 21x + 24

Answer: 3(4x2+7x+8)

  1. Highest common factor: 3
  2. 12x2 + 21x + 24 = 3(4x2 + 7x + 8)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab − 4a

Answer: 4a(3b − 1)

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

Answer: −4(x − 8)

  1. Highest common factor: −4
  2. −4x + 32 = −4(x − 8)
  3. Check by expanding the brackets.
8.Factorise fully: 3x2 − 12x − 6

Answer: 3(x2−4x−2)

  1. Highest common factor: 3
  2. 3x2 − 12x − 6 = 3(x2 − 4x − 2)
  3. Check by expanding the brackets.
9.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.
10.Factorise fully: −16x − 20

Answer: −4(4x + 5)

  1. Highest common factor: −4
  2. −16x − 20 = −4(4x + 5)
  3. Check by expanding the brackets.
11.Factorise fully: 3x2 − 18x − 18

Answer: 3(x2−6x−6)

  1. Highest common factor: 3
  2. 3x2 − 18x − 18 = 3(x2 − 6x − 6)
  3. Check by expanding the brackets.
12.Factorise fully: 3ab − 12a

Answer: 3a(b − 4)

  1. Highest common factor: 3a
  2. 3ab − 12a = 3a(b − 4)
  3. Check by expanding the brackets.
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