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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.Factorise fully: −40x + 48

Answer: −8(5x − 6)

  1. Highest common factor: −8
  2. −40x + 48 = −8(5x − 6)
  3. Check by expanding the brackets.
2.Factorise fully: 10x2 − 35x + 20

Answer: 5(2x2−7x+4)

  1. Highest common factor: 5
  2. 10x2 − 35x + 20 = 5(2x2 − 7x + 4)
  3. Check by expanding the brackets.
3.Factorise fully: 30ab − 35a

Answer: 5a(6b − 7)

  1. Highest common factor: 5a
  2. 30ab − 35a = 5a(6b − 7)
  3. Check by expanding the brackets.
4.Factorise fully: −18x + 27

Answer: −9(2x − 3)

  1. Highest common factor: −9
  2. −18x + 27 = −9(2x − 3)
  3. Check by expanding the brackets.
5.Factorise fully: 10x2 + 15x − 10

Answer: 5(2x2+3x−2)

  1. Highest common factor: 5
  2. 10x2 + 15x − 10 = 5(2x2 + 3x − 2)
  3. Check by expanding the brackets.
6.Factorise fully: 6ab − 10a

Answer: 2a(3b − 5)

  1. Highest common factor: 2a
  2. 6ab − 10a = 2a(3b − 5)
  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: 8x2 − 2x + 18

Answer: 2(4x2−x+9)

  1. Highest common factor: 2
  2. 8x2 − 2x + 18 = 2(4x2 − x + 9)
  3. Check by expanding the brackets.
9.Factorise fully: 5ab + 20a

Answer: 5a(b + 4)

  1. Highest common factor: 5a
  2. 5ab + 20a = 5a(b + 4)
  3. Check by expanding the brackets.
10.Factorise fully: −18x + 63

Answer: −9(2x − 7)

  1. Highest common factor: −9
  2. −18x + 63 = −9(2x − 7)
  3. Check by expanding the brackets.
11.Factorise fully: 15x2 + 15x − 25

Answer: 5(3x2+3x−5)

  1. Highest common factor: 5
  2. 15x2 + 15x − 25 = 5(3x2 + 3x − 5)
  3. Check by expanding the brackets.
12.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.
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