Back to worksheets Maths Ages 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.
Student worksheet Answer key
Worksheet Studio Practice pack · Ages 16-18
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 9x + 18 = 0.
9 · 18 · 0 · Factored quadratic equations
2. Find the greater root of x² − 17x + 66 = 0.
17 · 66 · 0 · Factored quadratic equations
3. Find the greater root of x² − 5x + 6 = 0.
5 · 6 · 0 · Factored quadratic equations
4. Find the greater root of x² − 22x + 105 = 0.
22 · 105 · 0 · Factored quadratic equations
5. Find the greater root of x² − 14x + 33 = 0.
14 · 33 · 0 · Factored quadratic equations
6. Find the greater root of x² − 10x + 21 = 0.
10 · 21 · 0 · Factored quadratic equations
7. Find the greater root of x² − 17x + 30 = 0.
17 · 30 · 0 · Factored quadratic equations
8. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
9. Find the greater root of x² − 20x + 91 = 0.
20 · 91 · 0 · Factored quadratic equations
10. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
11. Find the greater root of x² − 16x + 39 = 0.
16 · 39 · 0 · Factored quadratic equations
12. Find the greater root of x² − 5x + 4 = 0.
5 · 4 · 0 · Factored quadratic equations
12 questions · Seed 57 · Age guidance, not curriculum certification
View the answer key Worksheet Studio Answer key · Ages 16-18
Factored quadratic equations Answers and reasoning. Review before teaching.
1. Find the greater root of x² − 9x + 18 = 0.
6 Factorise into (x − 3)(x − 6) = 0. The roots are 3 and 6, so the greater root is 6.
2. Find the greater root of x² − 17x + 66 = 0.
11 Factorise into (x − 6)(x − 11) = 0. The roots are 6 and 11, so the greater root is 11.
3. Find the greater root of x² − 5x + 6 = 0.
3 Factorise into (x − 2)(x − 3) = 0. The roots are 2 and 3, so the greater root is 3.
4. 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.
5. 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.
6. Find the greater root of x² − 10x + 21 = 0.
7 Factorise into (x − 3)(x − 7) = 0. The roots are 3 and 7, so the greater root is 7.
7. Find the greater root of x² − 17x + 30 = 0.
15 Factorise into (x − 2)(x − 15) = 0. The roots are 2 and 15, so the greater root is 15.
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. 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.
10. Find the greater root of x² − 12x + 35 = 0.
7 Factorise into (x − 5)(x − 7) = 0. The roots are 5 and 7, so the greater root is 7.
11. Find the greater root of x² − 16x + 39 = 0.
13 Factorise into (x − 3)(x − 13) = 0. The roots are 3 and 13, so the greater root is 13.
12. 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.
12 questions · Seed 57 · Age guidance, not curriculum certification
Worksheet Studio Practice pack · Ages 16-18
Factored quadratic equations Take your time. Show your thinking.
1. Find the greater root of x² − 9x + 18 = 0.
9 · 18 · 0 · Factored quadratic equations
2. Find the greater root of x² − 17x + 66 = 0.
17 · 66 · 0 · Factored quadratic equations
3. Find the greater root of x² − 5x + 6 = 0.
5 · 6 · 0 · Factored quadratic equations
4. Find the greater root of x² − 22x + 105 = 0.
22 · 105 · 0 · Factored quadratic equations
5. Find the greater root of x² − 14x + 33 = 0.
14 · 33 · 0 · Factored quadratic equations
6. Find the greater root of x² − 10x + 21 = 0.
10 · 21 · 0 · Factored quadratic equations
7. Find the greater root of x² − 17x + 30 = 0.
17 · 30 · 0 · Factored quadratic equations
8. Find the greater root of x² − 17x + 70 = 0.
17 · 70 · 0 · Factored quadratic equations
9. Find the greater root of x² − 20x + 91 = 0.
20 · 91 · 0 · Factored quadratic equations
10. Find the greater root of x² − 12x + 35 = 0.
12 · 35 · 0 · Factored quadratic equations
11. Find the greater root of x² − 16x + 39 = 0.
16 · 39 · 0 · Factored quadratic equations
12. Find the greater root of x² − 5x + 4 = 0.
5 · 4 · 0 · Factored quadratic equations
12 questions · Seed 57 · Age guidance, not curriculum certification
Worksheet Studio Answer key · Ages 16-18
Factored quadratic equations Answers and reasoning. Review before teaching.
1. Find the greater root of x² − 9x + 18 = 0.
6 Factorise into (x − 3)(x − 6) = 0. The roots are 3 and 6, so the greater root is 6.
2. Find the greater root of x² − 17x + 66 = 0.
11 Factorise into (x − 6)(x − 11) = 0. The roots are 6 and 11, so the greater root is 11.
3. Find the greater root of x² − 5x + 6 = 0.
3 Factorise into (x − 2)(x − 3) = 0. The roots are 2 and 3, so the greater root is 3.
4. 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.
5. 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.
6. Find the greater root of x² − 10x + 21 = 0.
7 Factorise into (x − 3)(x − 7) = 0. The roots are 3 and 7, so the greater root is 7.
7. Find the greater root of x² − 17x + 30 = 0.
15 Factorise into (x − 2)(x − 15) = 0. The roots are 2 and 15, so the greater root is 15.
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. 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.
10. Find the greater root of x² − 12x + 35 = 0.
7 Factorise into (x − 5)(x − 7) = 0. The roots are 5 and 7, so the greater root is 7.
11. Find the greater root of x² − 16x + 39 = 0.
13 Factorise into (x − 3)(x − 13) = 0. The roots are 3 and 13, so the greater root is 13.
12. 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.
12 questions · Seed 57 · Age guidance, not curriculum certification
More maths worksheets Also in: 8th Grade Worksheets