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Factorise four-term expressions by grouping

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 by grouping: 5x² + 15x − 2x − 6

    • A. (5x − 2)(x + 3)
    • B. (5x + 2)(x − 3)
    • C. (5x + 3)(x − 2)
    • D. (x − 2)(x + 3)

  2. Question 2

    Factorise: xy − 1x − 1y + 1

    • A. (x + 1)(y + 1)
    • B. (x − 1)(y − 1)
    • C. (x − 1)(y + 1)

  3. Question 3

    Factorise by grouping: x³ + 6x² + 5x + 30

    • A. (x² + 5)(x − 6)
    • B. (x² + 6)(x + 5)
    • C. (x² + 5)(x + 6)
    • D. (x + 6)(x + 5)

  4. Question 4

    Factorise by grouping: 3x² − 18x + 7x − 42

    • A. (x + 7)(x − 6)
    • B. (3x − 6)(x + 7)
    • C. (3x + 7)(x − 6)
    • D. (3x − 7)(x + 6)

  5. Question 5

    Factorise: xy + 4x − 5y − 20

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

  6. Question 6

    Factorise by grouping: x³ + 5x² + 5x + 25

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

  7. Question 7

    Factorise by grouping: 4x² − 8x − 7x + 14

    • A. (4x − 7)(x − 2)
    • B. (4x + 7)(x + 2)
    • C. (x − 7)(x − 2)
    • D. (4x − 7)(x + 2)

  8. Question 8

    Factorise: xy − 6x − 4y + 24

    • A. (x − 4)(y − 6)
    • B. (x − 6)(y − 4)
    • C. (x + 4)(y + 6)
    • D. (x − 4)(y + 6)

  9. Question 9

    Factorise by grouping: x³ + x² + 6x + 6

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

  10. Question 10

    Factorise by grouping: 2x² + 6x + 5x + 15

    • A. (2x + 15)(x + 1)
    • B. (x + 5)(x + 3)
    • C. (2x + 5)(x + 3)
    • D. (2x + 3)(x + 5)

  11. Question 11

    Factorise: xy − 5x + 5y − 25

    • A. (x − 5)(y + 5)
    • B. (x + 5)(y − 5)
    • C. (x + 5)(y + 5)

  12. Question 12

    Factorise by grouping: x³ + 4x² − 3x − 12

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

  13. Question 13

    Factorise by grouping: 4x² − 24x − 5x + 30

    • A. (4x − 6)(x − 5)
    • B. (4x + 5)(x + 6)
    • C. (4x − 5)(x + 6)
    • D. (4x − 5)(x − 6)

  14. Question 14

    Factorise: xy + 1x − 3y − 3

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

  15. Question 15

    Factorise by grouping: x³ − 2x² − 4x + 8

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

  16. Question 16

    Factorise by grouping: 5x² − 5x − 1x + 1

    • A. (x − 1)(x − 1)
    • B. (5x + 1)(x + 1)
    • C. (5x − 1)(x − 1)
    • D. (5x − 1)(x + 1)

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Answer key: Factorise four-term expressions by grouping

  1. 1. A. (5x − 2)(x + 3)

  2. 2. B. (x − 1)(y − 1)

  3. 3. C. (x² + 5)(x + 6)

  4. 4. C. (3x + 7)(x − 6)

  5. 5. D. (x − 5)(y + 4)

  6. 6. B. (x² + 5)(x + 5)

  7. 7. A. (4x − 7)(x − 2)

  8. 8. A. (x − 4)(y − 6)

  9. 9. C. (x² + 6)(x + 1)

  10. 10. C. (2x + 5)(x + 3)

  11. 11. B. (x + 5)(y − 5)

  12. 12. C. (x² − 3)(x + 4)

  13. 13. D. (4x − 5)(x − 6)

  14. 14. D. (x − 3)(y + 1)

  15. 15. A. (x² − 4)(x − 2)

  16. 16. C. (5x − 1)(x − 1)