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

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

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Algebraic Expressions

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

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

1.Factorise fully: −4x + 12

Answer: −4(x − 3)

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

Answer: 2(x2+6x−8)

  1. Highest common factor: 2
  2. 2x2 + 12x − 16 = 2(x2 + 6x − 8)
  3. Check by expanding the brackets.
3.Factorise fully: 25ab + 15a

Answer: 5a(5b + 3)

  1. Highest common factor: 5a
  2. 25ab + 15a = 5a(5b + 3)
  3. Check by expanding the brackets.
4.Factorise fully: −20x + 12

Answer: −4(5x − 3)

  1. Highest common factor: −4
  2. −20x + 12 = −4(5x − 3)
  3. Check by expanding the brackets.
5.Factorise fully: 6x2 + 21x − 12

Answer: 3(2x2+7x−4)

  1. Highest common factor: 3
  2. 6x2 + 21x − 12 = 3(2x2 + 7x − 4)
  3. Check by expanding the brackets.
6.Factorise fully: 20ab + 45a

Answer: 5a(4b + 9)

  1. Highest common factor: 5a
  2. 20ab + 45a = 5a(4b + 9)
  3. Check by expanding the brackets.
7.Factorise fully: −6x + 30

Answer: −6(x − 5)

  1. Highest common factor: −6
  2. −6x + 30 = −6(x − 5)
  3. Check by expanding the brackets.
8.Factorise fully: 8x2 − 2x + 14

Answer: 2(4x2−x+7)

  1. Highest common factor: 2
  2. 8x2 − 2x + 14 = 2(4x2 − x + 7)
  3. Check by expanding the brackets.
9.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.
10.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.
11.Factorise fully: 12x2 + 9x − 21

Answer: 3(4x2+3x−7)

  1. Highest common factor: 3
  2. 12x2 + 9x − 21 = 3(4x2 + 3x − 7)
  3. Check by expanding the brackets.
12.Factorise fully: 18ab + 21a

Answer: 3a(6b + 7)

  1. Highest common factor: 3a
  2. 18ab + 21a = 3a(6b + 7)
  3. Check by expanding the brackets.
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