Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
MathsAges 13-15

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.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Factored quadratic equations

Take your time. Show your thinking.

  1. 1. Find the greater root of x² − 8x + 15 = 0.

    8 · 15 · 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 − 18x + 45 = 0.

    18 · 45 · 0 · Factored quadratic equations

  4. 4. Find the greater root of x² − 21x + 98 = 0.

    21 · 98 · 0 · Factored quadratic equations

  5. 5. Find the greater root of x² − 10x + 24 = 0.

    10 · 24 · 0 · Factored quadratic equations

  6. 6. Find the greater root of x² − 13x + 36 = 0.

    13 · 36 · 0 · Factored quadratic equations

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

    12 · 20 · 0 · Factored quadratic equations

  8. 8. Find the greater root of x² − 17x + 70 = 0.

    17 · 70 · 0 · Factored quadratic equations

  9. 9. Find the greater root of x² − 11x + 24 = 0.

    11 · 24 · 0 · Factored quadratic equations

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

    9 · 14 · 0 · Factored quadratic equations

  11. 11. Find the greater root of x² − 15x + 44 = 0.

    15 · 44 · 0 · Factored quadratic equations

  12. 12. Find the greater root of x² − 12x + 27 = 0.

    12 · 27 · 0 · Factored quadratic equations
12 questions · Seed 53 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Factored quadratic equations

Answers and reasoning. Review before teaching.

  1. 1. Find the greater root of x² − 8x + 15 = 0.

    5

    Factorise into (x − 3)(x − 5) = 0. The roots are 3 and 5, so the greater root is 5.

  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 − 18x + 45 = 0.

    15

    Factorise into (x − 3)(x − 15) = 0. The roots are 3 and 15, so the greater root is 15.

  4. 4. Find the greater root of x² − 21x + 98 = 0.

    14

    Factorise into (x − 7)(x − 14) = 0. The roots are 7 and 14, so the greater root is 14.

  5. 5. Find the greater root of x² − 10x + 24 = 0.

    6

    Factorise into (x − 4)(x − 6) = 0. The roots are 4 and 6, so the greater root is 6.

  6. 6. Find the greater root of x² − 13x + 36 = 0.

    9

    Factorise into (x − 4)(x − 9) = 0. The roots are 4 and 9, so the greater root is 9.

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

    10

    Factorise into (x − 2)(x − 10) = 0. The roots are 2 and 10, so the greater root is 10.

  8. 8. Find the greater root of x² − 17x + 70 = 0.

    10

    Factorise into (x − 7)(x − 10) = 0. The roots are 7 and 10, so the greater root is 10.

  9. 9. Find the greater root of x² − 11x + 24 = 0.

    8

    Factorise into (x − 3)(x − 8) = 0. The roots are 3 and 8, so the greater root is 8.

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

    7

    Factorise into (x − 2)(x − 7) = 0. The roots are 2 and 7, so the greater root is 7.

  11. 11. Find the greater root of x² − 15x + 44 = 0.

    11

    Factorise into (x − 4)(x − 11) = 0. The roots are 4 and 11, so the greater root is 11.

  12. 12. Find the greater root of x² − 12x + 27 = 0.

    9

    Factorise into (x − 3)(x − 9) = 0. The roots are 3 and 9, so the greater root is 9.

12 questions · Seed 53 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Factored quadratic equations

Take your time. Show your thinking.

  1. 1. Find the greater root of x² − 8x + 15 = 0.

    8 · 15 · 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 − 18x + 45 = 0.

    18 · 45 · 0 · Factored quadratic equations

  4. 4. Find the greater root of x² − 21x + 98 = 0.

    21 · 98 · 0 · Factored quadratic equations

  5. 5. Find the greater root of x² − 10x + 24 = 0.

    10 · 24 · 0 · Factored quadratic equations

  6. 6. Find the greater root of x² − 13x + 36 = 0.

    13 · 36 · 0 · Factored quadratic equations

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

    12 · 20 · 0 · Factored quadratic equations

  8. 8. Find the greater root of x² − 17x + 70 = 0.

    17 · 70 · 0 · Factored quadratic equations

  9. 9. Find the greater root of x² − 11x + 24 = 0.

    11 · 24 · 0 · Factored quadratic equations

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

    9 · 14 · 0 · Factored quadratic equations

  11. 11. Find the greater root of x² − 15x + 44 = 0.

    15 · 44 · 0 · Factored quadratic equations

  12. 12. Find the greater root of x² − 12x + 27 = 0.

    12 · 27 · 0 · Factored quadratic equations
12 questions · Seed 53 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Factored quadratic equations

Answers and reasoning. Review before teaching.

  1. 1. Find the greater root of x² − 8x + 15 = 0.

    5

    Factorise into (x − 3)(x − 5) = 0. The roots are 3 and 5, so the greater root is 5.

  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 − 18x + 45 = 0.

    15

    Factorise into (x − 3)(x − 15) = 0. The roots are 3 and 15, so the greater root is 15.

  4. 4. Find the greater root of x² − 21x + 98 = 0.

    14

    Factorise into (x − 7)(x − 14) = 0. The roots are 7 and 14, so the greater root is 14.

  5. 5. Find the greater root of x² − 10x + 24 = 0.

    6

    Factorise into (x − 4)(x − 6) = 0. The roots are 4 and 6, so the greater root is 6.

  6. 6. Find the greater root of x² − 13x + 36 = 0.

    9

    Factorise into (x − 4)(x − 9) = 0. The roots are 4 and 9, so the greater root is 9.

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

    10

    Factorise into (x − 2)(x − 10) = 0. The roots are 2 and 10, so the greater root is 10.

  8. 8. Find the greater root of x² − 17x + 70 = 0.

    10

    Factorise into (x − 7)(x − 10) = 0. The roots are 7 and 10, so the greater root is 10.

  9. 9. Find the greater root of x² − 11x + 24 = 0.

    8

    Factorise into (x − 3)(x − 8) = 0. The roots are 3 and 8, so the greater root is 8.

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

    7

    Factorise into (x − 2)(x − 7) = 0. The roots are 2 and 7, so the greater root is 7.

  11. 11. Find the greater root of x² − 15x + 44 = 0.

    11

    Factorise into (x − 4)(x − 11) = 0. The roots are 4 and 11, so the greater root is 11.

  12. 12. Find the greater root of x² − 12x + 27 = 0.

    9

    Factorise into (x − 3)(x − 9) = 0. The roots are 3 and 9, so the greater root is 9.

12 questions · Seed 53 · Age guidance, not curriculum certification