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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 2 — Answers

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

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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 2 — Answers

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

1.Factorise fully: −2x − 2

Answer: −2(x + 1)

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

Answer: 2(3x2−6x−5)

  1. Highest common factor: 2
  2. 6x2 − 12x − 10 = 2(3x2 − 6x − 5)
  3. Check by expanding the brackets.
3.Factorise fully: 3ab + 18a

Answer: 3a(b + 6)

  1. Highest common factor: 3a
  2. 3ab + 18a = 3a(b + 6)
  3. Check by expanding the brackets.
4.Factorise fully: −12x − 20

Answer: −4(3x + 5)

  1. Highest common factor: −4
  2. −12x − 20 = −4(3x + 5)
  3. Check by expanding the brackets.
5.Factorise fully: 24x2 + 42x − 36

Answer: 6(4x2+7x−6)

  1. Highest common factor: 6
  2. 24x2 + 42x − 36 = 6(4x2 + 7x − 6)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab − 15a

Answer: 3a(4b − 5)

  1. Highest common factor: 3a
  2. 12ab − 15a = 3a(4b − 5)
  3. Check by expanding the brackets.
7.Factorise fully: −2x − 14

Answer: −2(x + 7)

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

Answer: 2(x2+4x+7)

  1. Highest common factor: 2
  2. 2x2 + 8x + 14 = 2(x2 + 4x + 7)
  3. Check by expanding the brackets.
9.Factorise fully: 24ab − 30a

Answer: 6a(4b − 5)

  1. Highest common factor: 6a
  2. 24ab − 30a = 6a(4b − 5)
  3. Check by expanding the brackets.
10.Factorise fully: −24x + 4

Answer: −4(6x − 1)

  1. Highest common factor: −4
  2. −24x + 4 = −4(6x − 1)
  3. Check by expanding the brackets.
11.Factorise fully: 4x2 − 16x − 16

Answer: 4(x2−4x−4)

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

Answer: 4a(3b − 5)

  1. Highest common factor: 4a
  2. 12ab − 20a = 4a(3b − 5)
  3. Check by expanding the brackets.
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