Back to worksheets Maths Ages 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.
Student worksheet Answer key
Worksheet Studio Practice pack · Ages 13-15
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 8x + 12 = 0.
8 · 12 · 0 · Factored quadratic equations
2. Find the greater root of x² − 15x + 44 = 0.
15 · 44 · 0 · Factored quadratic equations
3. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
4. Find the greater root of x² − 17x + 72 = 0.
17 · 72 · 0 · Factored quadratic equations
5. Find the greater root of x² − 10x + 24 = 0.
10 · 24 · 0 · Factored quadratic equations
6. Find the greater root of x² − 20x + 91 = 0.
20 · 91 · 0 · Factored quadratic equations
7. Find the greater root of x² − 9x + 8 = 0.
9 · 8 · 0 · Factored quadratic equations
8. Find the greater root of x² − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
9. Find the greater root of x² − 20x + 84 = 0.
20 · 84 · 0 · Factored quadratic equations
10. Find the greater root of x² − 22x + 105 = 0.
22 · 105 · 0 · Factored quadratic equations
11. Find the greater root of x² − 13x + 40 = 0.
13 · 40 · 0 · Factored quadratic equations
12. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
12 questions · Seed 47 · Age guidance, not curriculum certification
View the answer key Worksheet Studio Answer key · Ages 13-15
Factored quadratic equations Answers and reasoning. Review before teaching.
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. 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.
3. Find the greater root of x² − 11x + 18 = 0.
9 Factorise into (x − 2)(x − 9) = 0. The roots are 2 and 9, so the greater root is 9.
4. Find the greater root of x² − 17x + 72 = 0.
9 Factorise into (x − 8)(x − 9) = 0. The roots are 8 and 9, so the greater root is 9.
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. Find the greater root of x² − 20x + 91 = 0.
13 Factorise into (x − 7)(x − 13) = 0. The roots are 7 and 13, so the greater root is 13.
7. Find the greater root of x² − 9x + 8 = 0.
8 Factorise into (x − 1)(x − 8) = 0. The roots are 1 and 8, so the greater root is 8.
8. Find the greater root of x² − 19x + 84 = 0.
12 Factorise into (x − 7)(x − 12) = 0. The roots are 7 and 12, so the greater root is 12.
9. Find the greater root of x² − 20x + 84 = 0.
14 Factorise into (x − 6)(x − 14) = 0. The roots are 6 and 14, so the greater root is 14.
10. Find the greater root of x² − 22x + 105 = 0.
15 Factorise into (x − 7)(x − 15) = 0. The roots are 7 and 15, so the greater root is 15.
11. Find the greater root of x² − 13x + 40 = 0.
8 Factorise into (x − 5)(x − 8) = 0. The roots are 5 and 8, so the greater root is 8.
12. Find the greater root of x² − 3x + 2 = 0.
2 Factorise into (x − 1)(x − 2) = 0. The roots are 1 and 2, so the greater root is 2.
12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet Studio Practice pack · Ages 13-15
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 8x + 12 = 0.
8 · 12 · 0 · Factored quadratic equations
2. Find the greater root of x² − 15x + 44 = 0.
15 · 44 · 0 · Factored quadratic equations
3. Find the greater root of x² − 11x + 18 = 0.
11 · 18 · 0 · Factored quadratic equations
4. Find the greater root of x² − 17x + 72 = 0.
17 · 72 · 0 · Factored quadratic equations
5. Find the greater root of x² − 10x + 24 = 0.
10 · 24 · 0 · Factored quadratic equations
6. Find the greater root of x² − 20x + 91 = 0.
20 · 91 · 0 · Factored quadratic equations
7. Find the greater root of x² − 9x + 8 = 0.
9 · 8 · 0 · Factored quadratic equations
8. Find the greater root of x² − 19x + 84 = 0.
19 · 84 · 0 · Factored quadratic equations
9. Find the greater root of x² − 20x + 84 = 0.
20 · 84 · 0 · Factored quadratic equations
10. Find the greater root of x² − 22x + 105 = 0.
22 · 105 · 0 · Factored quadratic equations
11. Find the greater root of x² − 13x + 40 = 0.
13 · 40 · 0 · Factored quadratic equations
12. Find the greater root of x² − 3x + 2 = 0.
3 · 2 · 0 · Factored quadratic equations
12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet Studio Answer key · Ages 13-15
Factored quadratic equations Answers and reasoning. Review before teaching.
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. 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.
3. Find the greater root of x² − 11x + 18 = 0.
9 Factorise into (x − 2)(x − 9) = 0. The roots are 2 and 9, so the greater root is 9.
4. Find the greater root of x² − 17x + 72 = 0.
9 Factorise into (x − 8)(x − 9) = 0. The roots are 8 and 9, so the greater root is 9.
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. Find the greater root of x² − 20x + 91 = 0.
13 Factorise into (x − 7)(x − 13) = 0. The roots are 7 and 13, so the greater root is 13.
7. Find the greater root of x² − 9x + 8 = 0.
8 Factorise into (x − 1)(x − 8) = 0. The roots are 1 and 8, so the greater root is 8.
8. Find the greater root of x² − 19x + 84 = 0.
12 Factorise into (x − 7)(x − 12) = 0. The roots are 7 and 12, so the greater root is 12.
9. Find the greater root of x² − 20x + 84 = 0.
14 Factorise into (x − 6)(x − 14) = 0. The roots are 6 and 14, so the greater root is 14.
10. Find the greater root of x² − 22x + 105 = 0.
15 Factorise into (x − 7)(x − 15) = 0. The roots are 7 and 15, so the greater root is 15.
11. Find the greater root of x² − 13x + 40 = 0.
8 Factorise into (x − 5)(x − 8) = 0. The roots are 5 and 8, so the greater root is 8.
12. Find the greater root of x² − 3x + 2 = 0.
2 Factorise into (x − 1)(x − 2) = 0. The roots are 1 and 2, so the greater root is 2.
12 questions · Seed 47 · Age guidance, not curriculum certification
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