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Factorise fully

9th grade (Year 10 in England) · 16 questions · Common Core: HSA.SSE.A.2 · England: GCSE Higher Algebra

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  1. Question 1

    Ethan says x³ − 49x = x(x² − 49) is fully factorised. What is the full factorisation?

    • A. x(x² − 49)
    • B. (x + 7)(x − 7)
    • C. x(x + 7)(x − 7)
    • D. x(x − 7)²

  2. Question 2

    Factorise fully: 3x² − 9x − 12

    • A. (3x − 4)(x + 1)
    • B. 3(x + 4)(x − 1)
    • C. (x − 4)(x + 1)
    • D. 3(x − 4)(x + 1)

  3. Question 3

    Factorise fully: 4x² − 16

    • A. (4x + 2)(x − 2)
    • B. 4(x² − 4)
    • C. 4(x + 2)(x − 2)
    • D. 4(x − 2)²

  4. Question 4

    Leo says x³ − 81x = x(x² − 81) is fully factorised. What is the full factorisation?

    • A. (x + 9)(x − 9)
    • B. x(x² − 81)
    • C. x(x + 9)(x − 9)
    • D. x(x − 9)²

  5. Question 5

    Factorise fully: 2x² − 12x + 16

    • A. 2(x − 4)(x − 2)
    • B. (x − 4)(x − 2)
    • C. (2x − 4)(x − 2)
    • D. 2(x + 4)(x + 2)

  6. Question 6

    Factorise fully: 3x² − 48

    • A. (3x + 4)(x − 4)
    • B. 3(x + 4)(x − 4)
    • C. 3(x − 4)²
    • D. 3(x² − 16)

  7. Question 7

    Ana says x³ − 49x = x(x² − 49) is fully factorised. What is the full factorisation?

    • A. (x + 7)(x − 7)
    • B. x(x − 7)²
    • C. x²(x − 49)
    • D. x(x + 7)(x − 7)

  8. Question 8

    Factorise fully: 2x² − 72

    • A. 2(x² − 36)
    • B. 2(x − 6)(x + 6)
    • C. 2(x + 6)(x − 6)
    • D. (2x + 6)(x − 6)

  9. Question 9

    Factorise fully: 6x² − 54

    • A. (x + 18)(x − 3)
    • B. 6(x² − 9)
    • C. 6(x − 3)²
    • D. 6(x + 3)(x − 3)

  10. Question 10

    Daniel says x³ − 4x = x(x² − 4) is fully factorised. What is the full factorisation?

    • A. x(x² − 4)
    • B. x(x − 2)²
    • C. x²(x − 4)
    • D. x(x + 2)(x − 2)

  11. Question 11

    Factorise fully: 5x² − 80

    • A. (x − 4)(x + 4)
    • B. (5x − 4)(x + 4)
    • C. 5(x − 4)(x + 4)
    • D. 5(x² − 16)

  12. Question 12

    Factorise fully: 3x² − 192

    • A. 3(x + 8)(x − 8)
    • B. (3x + 8)(x − 8)
    • C. 3(x² − 64)
    • D. (x + 24)(x − 8)

  13. Question 13

    Ben says x³ − 64x = x(x² − 64) is fully factorised. What is the full factorisation?

    • A. x(x + 8)(x − 8)
    • B. x(x − 8)²
    • C. x(x² − 64)
    • D. (x + 8)(x − 8)

  14. Question 14

    Factorise fully: 2x² − 72

    • A. 2(x − 6)(x + 6)
    • B. (2x + 6)(x − 6)
    • C. 2(x² − 36)
    • D. 2(x + 6)(x − 6)

  15. Question 15

    Factorise fully: 6x² − 216

    • A. 6(x − 6)²
    • B. 6(x + 6)(x − 6)
    • C. (6x + 6)(x − 6)
    • D. (x + 36)(x − 6)

  16. Question 16

    Ana says x³ − 100x = x(x² − 100) is fully factorised. What is the full factorisation?

    • A. x(x − 10)²
    • B. x(x + 10)(x − 10)
    • C. (x + 10)(x − 10)
    • D. x(x² − 100)

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  1. x(x + 7)(x − 7)
  2. 3(x − 4)(x + 1)
  3. 4(x + 2)(x − 2)
  4. x(x + 9)(x − 9)
  5. 2(x − 4)(x − 2)
  6. 3(x + 4)(x − 4)
  7. x(x + 7)(x − 7)
  8. 2(x + 6)(x − 6)
  9. 6(x + 3)(x − 3)
  10. x(x + 2)(x − 2)
  11. 5(x − 4)(x + 4)
  12. 3(x + 8)(x − 8)
  13. x(x + 8)(x − 8)
  14. 2(x + 6)(x − 6)
  15. 6(x + 6)(x − 6)
  16. x(x + 10)(x − 10)