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Factorise fully, including variable and negative common factors

7th grade (Year 8 in England) · 16 questions · Common Core: 7.EE.A.1 · England: KS3 Algebra, GCSE Foundation Algebra

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Date

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  1. Question 1

    Chloe factorises 40x + 48 as 2(20x + 24). Is it fully factorised?

    • A. Yes
    • B. No, it should be 8(5x + 6)

  2. Question 2

    Factorise −3x − 27 by taking out a negative common factor.

    • A. −3(x + 9)
    • B. −3(x + 27)
    • C. 3(x + 9)
    • D. −3(x − 9)

  3. Question 3

    Factorise fully: 3xy + 6x

    • A. 3x(y + 2)
    • B. 3y(x + 2)
    • C. 3(xy + 2x)
    • D. x(3y + 6)

  4. Question 4

    Leo factorises 4x + 16 as 4(1x + 4). Is it fully factorised?

    • A. Yes
    • B. No, it should be 4(1x + 4)

  5. Question 5

    Factorise −3x − 18 by taking out a negative common factor.

    • A. −3(x + 18)
    • B. −3(x + 6)
    • C. −(3x − 18)
    • D. −3(x − 6)

  6. Question 6

    Factorise fully: 5xy + 35x

    • A. 5y(x + 7)
    • B. 5(xy + 7x)
    • C. 5x(y + 7)
    • D. x(5y + 35)

  7. Question 7

    Diego factorises 16x + 8 as 8(2x + 1). Is it fully factorised?

    • A. Yes
    • B. No, it should be 8(2x + 1)

  8. Question 8

    Factorise −5x − 15 by taking out a negative common factor.

    • A. −5(x + 15)
    • B. −5(x + 3)
    • C. −5(x − 3)
    • D. 5(x + 3)

  9. Question 9

    Factorise fully: 2xy + 10x

    • A. 2y(x + 5)
    • B. x(2y + 10)
    • C. 2x(y + 5)
    • D. 2x(y + 10)

  10. Question 10

    Aisha factorises 8x + 28 as 2(4x + 14). Is it fully factorised?

    • A. Yes
    • B. No, it should be 4(2x + 7)

  11. Question 11

    Factorise −2x − 6 by taking out a negative common factor.

    • A. 2(x + 3)
    • B. −2(x + 3)
    • C. −2(x − 3)
    • D. −(2x − 6)

  12. Question 12

    Factorise fully: 4xy + 12x

    • A. 4(xy + 3x)
    • B. 4y(x + 3)
    • C. 4x(y + 3)
    • D. 4x(y + 12)

  13. Question 13

    Zoe factorises 24x + 16 as 2(12x + 8). Is it fully factorised?

    • A. Yes
    • B. No, it should be 8(3x + 2)

  14. Question 14

    Factorise −6x − 12 by taking out a negative common factor.

    • A. −6(x + 2)
    • B. 6(x + 2)
    • C. −6(x + 12)
    • D. −6(x − 2)

  15. Question 15

    Factorise fully: 5xy + 10x

    • A. 5x(y + 10)
    • B. 5(xy + 2x)
    • C. 5y(x + 2)
    • D. 5x(y + 2)

  16. Question 16

    Zoe factorises 30x + 6 as 2(15x + 3). Is it fully factorised?

    • A. Yes
    • B. No, it should be 6(5x + 1)

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Answer key: Factorise fully, including variable and negative common factors

  1. 1. B. No, it should be 8(5x + 6)

  2. 2. A. −3(x + 9)

  3. 3. A. 3x(y + 2)

  4. 4. A. Yes

  5. 5. B. −3(x + 6)

  6. 6. C. 5x(y + 7)

  7. 7. A. Yes

  8. 8. B. −5(x + 3)

  9. 9. C. 2x(y + 5)

  10. 10. B. No, it should be 4(2x + 7)

  11. 11. B. −2(x + 3)

  12. 12. C. 4x(y + 3)

  13. 13. B. No, it should be 8(3x + 2)

  14. 14. A. −6(x + 2)

  15. 15. D. 5x(y + 2)

  16. 16. B. No, it should be 6(5x + 1)