Algebra 1: Factoring Polynomials Topic F3: Factoring Trinomials in the Form x2 + bx + c | VERSION A
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Factor the following trinomials.
1. 𝑎! + 5𝑎 + 6
2. 𝑦! − 8𝑦 + 12
3. 𝑦! − 2𝑦 − 15
4. 𝑥! + 𝑥 − 12
5. 𝑟! − 8𝑟 + 12
Factor the following problems completely. First factor out the greatest common factors, and then factor the remaining trinomials.
6. 10𝑟! + 70𝑟 + 100
7. 5𝑦! − 10𝑦 − 175
8. 3𝑎! − 33𝑎 + 90
9. 10𝑎! + 10𝑎 − 120
10. 𝑟! + 1𝑟! − 42𝑟!
Algebra 1: Factoring Polynomials Topic F3: Factoring Trinomials in the Form x2 + bx + c | VERSION A
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11. 10𝑥! + 30𝑥! + 20𝑥
12. −𝑎! − 7𝑎! − 12𝑎!
Factor the following:
13. 𝑥! + 13𝑥𝑏 + 42𝑏!
14. 𝑎! + 9𝑎! + 20
15. 𝑟! + 3𝑟! − 10
16. 𝑥! + 170𝑥 − 6000
17. 𝑦! − 𝑦 + !!
18. If one of the factors of 𝑟! + 21𝑟 + 98 is 𝑟 + 7, what is the other factor?
19. What is the polynomial, when factored, that gives 2𝑟 + 6 𝑟 + 7 ?
20. What is the polynomial, when factored, that gives 6𝑟 + 3 𝑟 + 5 ?
Algebra 1: Factoring Polynomials Topic F3: Factoring Trinomials in the Form x2 + bx + c | VERSION A
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Name: _______________________________________
Factor the following trinomials.
1. 𝑎! + 5𝑎 + 6 𝑎 + 2 𝑎 + 3
2. 𝑦! − 8𝑦 + 12 𝑦 − 2 𝑦 − 6
3. 𝑦! − 2𝑦 − 15 𝑦 − 5 𝑦 + 3
4. 𝑥! + 𝑥 − 12 𝑥 − 3 𝑥 + 4
5. 𝑟! − 8𝑟 + 12 𝑟 − 2 𝑟 − 6
Factor the following problems completely. First factor out the greatest common factors, and then factor the remaining trinomials.
6. 10𝑟! + 70𝑟 + 100 10 𝑟 + 2 𝑟 + 5
7. 5𝑦! − 10𝑦 − 175 5 𝑦 − 7 𝑦 + 5
8. 3𝑎! − 33𝑎 + 90 3 𝑎 − 5 𝑎 − 6
9. 10𝑎! + 10𝑎 − 120 10 𝑎 − 3 𝑎 + 4
10. 𝑟! + 1𝑟! − 42𝑟! 𝑟! 𝑟 − 6 𝑟 + 7
Algebra 1: Factoring Polynomials Topic F3: Factoring Trinomials in the Form x2 + bx + c | VERSION A
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11. 10𝑥! + 30𝑥! + 20𝑥 10𝑥 𝑥 + 2 𝑥 + 1
12. −𝑎! − 7𝑎! − 12𝑎! −𝑎! 𝑎 + 4 𝑎 + 3
Factor the following:
13. 𝑥! + 13𝑥𝑏 + 42𝑏! 𝑥 + 6𝑏 𝑥 + 7𝑏
14. 𝑎! + 9𝑎! + 20 𝑎! + 4 𝑎! + 5
15. 𝑟! + 3𝑟! − 10 𝑟! + 5 𝑟! − 2
16. 𝑥! + 170𝑥 − 6000 𝑥 − 30 𝑥 + 200
17. 𝑦! − 𝑦 + !! 𝑦 − 1
2!
18. If one of the factors of 𝑟! + 21𝑟 + 98 is 𝑟 + 7, what is the other factor? 𝑟 + 14
19. What is the polynomial, when factored, that gives 2𝑟 + 6 𝑟 + 7 ? 2𝑟! + 20𝑟 + 42
20. What is the polynomial, when factored, that gives 6𝑟 + 3 𝑟 + 5 ? 6𝑟! + 33𝑟 + 15
