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