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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

    Factorise fully: 3x² − 147

    • A. 3(x² − 49)
    • B. (3x + 7)(x − 7)
    • C. 3(x + 7)(x − 7)
    • D. 3(x − 7)²

  2. Question 2

    Factorise fully: 2x² − 14x + 12

    • A. 2(x + 6)(x + 1)
    • B. 2(x² − 7x + 6)
    • C. 2(x − 6)(x − 1)
    • D. (2x − 6)(x − 1)

  3. Question 3

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

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

  4. Question 4

    Factorise fully: 2x² − 32

    • A. 2(x + 4)(x − 4)
    • B. (x + 8)(x − 4)
    • C. 2(x² − 16)
    • D. 2(x − 4)²

  5. Question 5

    Factorise fully: 5x² − 10x − 75

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

  6. Question 6

    Isla says x³ − 16x = x(x² − 16) is fully factorised. What is the full factorisation?

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

  7. Question 7

    Factorise fully: 5x² − 45

    • A. 5(x + 3)(x − 3)
    • B. 5(x² − 9)
    • C. (x + 15)(x − 3)
    • D. (5x + 3)(x − 3)

  8. Question 8

    Factorise fully: 2x² + 6x − 20

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

  9. Question 9

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

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

  10. Question 10

    Factorise fully: 2x² − 18

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

  11. Question 11

    Factorise fully: 3x² + 27x + 60

    • A. 3(x + 5)(x + 4)
    • B. (x + 5)(x + 4)
    • C. 3(x − 5)(x − 4)
    • D. (3x + 5)(x + 4)

  12. Question 12

    Leo says x³ − 16x = x(x² − 16) is fully factorised. What is the full factorisation?

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

  13. Question 13

    Factorise fully: 4x² − 4

    • A. (4x + 1)(x − 1)
    • B. (x + 4)(x − 1)
    • C. 4(x² − 1)
    • D. 4(x + 1)(x − 1)

  14. Question 14

    Factorise fully: 4x² − 4x − 24

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

  15. Question 15

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

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

  16. Question 16

    Factorise fully: 5x² − 320

    • A. 5(x + 8)(x − 8)
    • B. 5(x − 8)²
    • C. (5x + 8)(x − 8)
    • D. 5(x² − 64)

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Answer key: Factorise fully

  1. 1. C. 3(x + 7)(x − 7)

  2. 2. C. 2(x − 6)(x − 1)

  3. 3. A. x(x + 9)(x − 9)

  4. 4. A. 2(x + 4)(x − 4)

  5. 5. A. 5(x − 5)(x + 3)

  6. 6. D. x(x + 4)(x − 4)

  7. 7. A. 5(x + 3)(x − 3)

  8. 8. A. 2(x + 5)(x − 2)

  9. 9. A. x(x + 7)(x − 7)

  10. 10. D. 2(x + 3)(x − 3)

  11. 11. A. 3(x + 5)(x + 4)

  12. 12. B. x(x + 4)(x − 4)

  13. 13. D. 4(x + 1)(x − 1)

  14. 14. A. 4(x − 3)(x + 2)

  15. 15. C. x(x + 10)(x − 10)

  16. 16. A. 5(x + 8)(x − 8)