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MathsAges 16-18

Factored quadratic equations

Solve a monic quadratic equation by factorising into two linear brackets and identifying the greater root. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Factored quadratic equations

Take your time. Show your thinking.

  1. 1. Find the greater root of x² − 8x + 12 = 0.

    8 · 12 · 0 · Factored quadratic equations

  2. 2. Find the greater root of x² − 13x + 42 = 0.

    13 · 42 · 0 · Factored quadratic equations

  3. 3. Find the greater root of x² − 23x + 120 = 0.

    23 · 120 · 0 · Factored quadratic equations

  4. 4. Find the greater root of x² − 17x + 52 = 0.

    17 · 52 · 0 · Factored quadratic equations

  5. 5. Find the greater root of x² − 5x + 4 = 0.

    5 · 4 · 0 · Factored quadratic equations

  6. 6. Find the greater root of x² − 7x + 12 = 0.

    7 · 12 · 0 · Factored quadratic equations

  7. 7. Find the greater root of x² − 16x + 28 = 0.

    16 · 28 · 0 · Factored quadratic equations

  8. 8. Find the greater root of x² − 14x + 33 = 0.

    14 · 33 · 0 · Factored quadratic equations

  9. 9. Find the greater root of x² − 14x + 24 = 0.

    14 · 24 · 0 · Factored quadratic equations

  10. 10. Find the greater root of x² − 6x + 5 = 0.

    6 · 5 · 0 · Factored quadratic equations

  11. 11. Find the greater root of x² − 15x + 54 = 0.

    15 · 54 · 0 · Factored quadratic equations

  12. 12. Find the greater root of x² − 9x + 20 = 0.

    9 · 20 · 0 · Factored quadratic equations
12 questions · Seed 54 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Factored quadratic equations

Answers and reasoning. Review before teaching.

  1. 1. Find the greater root of x² − 8x + 12 = 0.

    6

    Factorise into (x − 2)(x − 6) = 0. The roots are 2 and 6, so the greater root is 6.

  2. 2. Find the greater root of x² − 13x + 42 = 0.

    7

    Factorise into (x − 6)(x − 7) = 0. The roots are 6 and 7, so the greater root is 7.

  3. 3. Find the greater root of x² − 23x + 120 = 0.

    15

    Factorise into (x − 8)(x − 15) = 0. The roots are 8 and 15, so the greater root is 15.

  4. 4. Find the greater root of x² − 17x + 52 = 0.

    13

    Factorise into (x − 4)(x − 13) = 0. The roots are 4 and 13, so the greater root is 13.

  5. 5. Find the greater root of x² − 5x + 4 = 0.

    4

    Factorise into (x − 1)(x − 4) = 0. The roots are 1 and 4, so the greater root is 4.

  6. 6. Find the greater root of x² − 7x + 12 = 0.

    4

    Factorise into (x − 3)(x − 4) = 0. The roots are 3 and 4, so the greater root is 4.

  7. 7. Find the greater root of x² − 16x + 28 = 0.

    14

    Factorise into (x − 2)(x − 14) = 0. The roots are 2 and 14, so the greater root is 14.

  8. 8. Find the greater root of x² − 14x + 33 = 0.

    11

    Factorise into (x − 3)(x − 11) = 0. The roots are 3 and 11, so the greater root is 11.

  9. 9. Find the greater root of x² − 14x + 24 = 0.

    12

    Factorise into (x − 2)(x − 12) = 0. The roots are 2 and 12, so the greater root is 12.

  10. 10. Find the greater root of x² − 6x + 5 = 0.

    5

    Factorise into (x − 1)(x − 5) = 0. The roots are 1 and 5, so the greater root is 5.

  11. 11. Find the greater root of x² − 15x + 54 = 0.

    9

    Factorise into (x − 6)(x − 9) = 0. The roots are 6 and 9, so the greater root is 9.

  12. 12. Find the greater root of x² − 9x + 20 = 0.

    5

    Factorise into (x − 4)(x − 5) = 0. The roots are 4 and 5, so the greater root is 5.

12 questions · Seed 54 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Factored quadratic equations

Take your time. Show your thinking.

  1. 1. Find the greater root of x² − 8x + 12 = 0.

    8 · 12 · 0 · Factored quadratic equations

  2. 2. Find the greater root of x² − 13x + 42 = 0.

    13 · 42 · 0 · Factored quadratic equations

  3. 3. Find the greater root of x² − 23x + 120 = 0.

    23 · 120 · 0 · Factored quadratic equations

  4. 4. Find the greater root of x² − 17x + 52 = 0.

    17 · 52 · 0 · Factored quadratic equations

  5. 5. Find the greater root of x² − 5x + 4 = 0.

    5 · 4 · 0 · Factored quadratic equations

  6. 6. Find the greater root of x² − 7x + 12 = 0.

    7 · 12 · 0 · Factored quadratic equations

  7. 7. Find the greater root of x² − 16x + 28 = 0.

    16 · 28 · 0 · Factored quadratic equations

  8. 8. Find the greater root of x² − 14x + 33 = 0.

    14 · 33 · 0 · Factored quadratic equations

  9. 9. Find the greater root of x² − 14x + 24 = 0.

    14 · 24 · 0 · Factored quadratic equations

  10. 10. Find the greater root of x² − 6x + 5 = 0.

    6 · 5 · 0 · Factored quadratic equations

  11. 11. Find the greater root of x² − 15x + 54 = 0.

    15 · 54 · 0 · Factored quadratic equations

  12. 12. Find the greater root of x² − 9x + 20 = 0.

    9 · 20 · 0 · Factored quadratic equations
12 questions · Seed 54 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Factored quadratic equations

Answers and reasoning. Review before teaching.

  1. 1. Find the greater root of x² − 8x + 12 = 0.

    6

    Factorise into (x − 2)(x − 6) = 0. The roots are 2 and 6, so the greater root is 6.

  2. 2. Find the greater root of x² − 13x + 42 = 0.

    7

    Factorise into (x − 6)(x − 7) = 0. The roots are 6 and 7, so the greater root is 7.

  3. 3. Find the greater root of x² − 23x + 120 = 0.

    15

    Factorise into (x − 8)(x − 15) = 0. The roots are 8 and 15, so the greater root is 15.

  4. 4. Find the greater root of x² − 17x + 52 = 0.

    13

    Factorise into (x − 4)(x − 13) = 0. The roots are 4 and 13, so the greater root is 13.

  5. 5. Find the greater root of x² − 5x + 4 = 0.

    4

    Factorise into (x − 1)(x − 4) = 0. The roots are 1 and 4, so the greater root is 4.

  6. 6. Find the greater root of x² − 7x + 12 = 0.

    4

    Factorise into (x − 3)(x − 4) = 0. The roots are 3 and 4, so the greater root is 4.

  7. 7. Find the greater root of x² − 16x + 28 = 0.

    14

    Factorise into (x − 2)(x − 14) = 0. The roots are 2 and 14, so the greater root is 14.

  8. 8. Find the greater root of x² − 14x + 33 = 0.

    11

    Factorise into (x − 3)(x − 11) = 0. The roots are 3 and 11, so the greater root is 11.

  9. 9. Find the greater root of x² − 14x + 24 = 0.

    12

    Factorise into (x − 2)(x − 12) = 0. The roots are 2 and 12, so the greater root is 12.

  10. 10. Find the greater root of x² − 6x + 5 = 0.

    5

    Factorise into (x − 1)(x − 5) = 0. The roots are 1 and 5, so the greater root is 5.

  11. 11. Find the greater root of x² − 15x + 54 = 0.

    9

    Factorise into (x − 6)(x − 9) = 0. The roots are 6 and 9, so the greater root is 9.

  12. 12. Find the greater root of x² − 9x + 20 = 0.

    5

    Factorise into (x − 4)(x − 5) = 0. The roots are 4 and 5, so the greater root is 5.

12 questions · Seed 54 · Age guidance, not curriculum certification