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Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F4: Factoring Trinomials in the Form ax2 + bx + c | VERSION A Factor the following trinomials. 1.
2.
3.
4.
6.
18𝑎 ! + 9𝑎 − 5 7.
12𝑏 ! + 11𝑏𝑥 − 15𝑥 ! 8.
−25𝑥 ! + 30𝑥 − 9 3𝑎 ! + 11𝑎 + 10 3𝑥 ! − 4𝑥 − 4 6𝑥 ! − 5𝑥 − 6 !
!
6𝑎 + 7𝑎𝑟 + 2𝑟 Factor the following trinomials completely. Look first for the greatest common factor. 9.
5.
6𝑦 ! + 32𝑦 + 42 20𝑟 ! + 41𝑟𝑥 + 20𝑥 ! 10. 6𝑥 ! − 5𝑥 ! − 25𝑥 www.varsitylearning.com 1 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F4: Factoring Trinomials in the Form ax2 + bx + c | VERSION A 11. 15𝑥 ! + 8𝑥 ! + 𝑥 ! Factor the following trinomials. 16. 20𝑎 ! + 41𝑎 + 20 12. 20𝑟 ! 𝑦 ! − 48𝑟𝑦 ! − 36𝑦 ! 17. 15𝑥 ! − 34𝑥 + 15 13. What polynomial factors to 𝑥 + 5 𝑥 − 5 𝑥 ! + 25 ? 18. 6𝑦 ! + 16𝑦 − 6 At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet) of the coin tossed in the air is: ℎ = 6 + 29𝑡 − 16𝑡 ! 14. Use the factored form of the equation to find the height of the quarter after 1 second: 15. Use the factored form of the equation to find the height of the quarter after 2 seconds: 19. 15𝑟 ! − 16𝑟 ! − 15𝑟 ! 20. 15𝑎 ! + 84𝑎 ! + 45𝑎 ! www.varsitylearning.com 2 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F4: Factoring Trinomials in the Form ax2 + bx + c | VERSION A Factor the following trinomials. 1.
2.
3.
4.
6.
18𝑎 ! + 9𝑎 − 5 6𝑎 + 5 3𝑎 − 1 7.
12𝑏 ! + 11𝑏𝑥 − 15𝑥 ! 3𝑏 + 5𝑥 4𝑏 − 3𝑥 8.
−25𝑥 ! + 30𝑥 − 9 −5𝑥 + 3 5𝑥 − 3 3𝑎 ! + 11𝑎 + 10 3𝑎 + 5 𝑎 + 2 3𝑥 ! − 4𝑥 − 4 3𝑥 + 2 𝑥 − 2 6𝑥 ! − 5𝑥 − 6 3𝑥 + 2 2𝑥 − 3 !
!
6𝑎 + 7𝑎𝑟 + 2𝑟 2𝑎 + 𝑟 3𝑎 + 2𝑟 Factor the following trinomials completely. Look first for the greatest common factor. 9.
5.
6𝑦 ! + 32𝑦 + 42 2 3𝑦 + 7 𝑦 + 3 20𝑟 ! + 41𝑟𝑥 + 20𝑥 ! 5𝑟 + 4𝑥 4𝑟 + 5𝑥 10. 6𝑥 ! − 5𝑥 ! − 25𝑥 𝑥 ⋅ 3𝑥 + 5 2𝑥 − 5 www.varsitylearning.com 3 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F4: Factoring Trinomials in the Form ax2 + bx + c | VERSION A 11. 15𝑥 ! + 8𝑥 ! + 𝑥 ! 𝑥 ! 5𝑥 + 1 3𝑥 + 1 Factor the following trinomials. 16. 20𝑎 ! + 41𝑎 + 20 5𝑎 + 4 4𝑎 + 5 12. 20𝑟 ! 𝑦 ! − 48𝑟𝑦 ! − 36𝑦 ! 4𝑦 ! 5𝑟 + 3 𝑟 − 3 17. 15𝑥 ! − 34𝑥 + 15 3𝑥 − 5 5𝑥 − 3 13. What polynomial factors to 𝑥 + 5 𝑥 − 5 𝑥 ! + 25 ? 𝑥 ! − 625 18. 6𝑦 ! + 16𝑦 − 6 2 3𝑦 − 1 𝑦 + 3 At the beginning of every football game, the referee flips a coin to see who will kick off. The equation that gives the height (in feet) of the coin tossed in the air is: ℎ = 6 + 29𝑡 − 16𝑡 ! 19. 15𝑟 ! − 16𝑟 ! − 15𝑟 ! 𝑟 ! 5𝑟 + 3 3𝑟 − 5 14. Use the factored form of the equation to find the height of the quarter after 1 second: 19 15. Use the factored form of the equation to find the height of the quarter after 2 seconds: 0 20. 15𝑎 ! + 84𝑎 ! + 45𝑎 ! 3𝑎 ! 5𝑎 + 3 𝑎 + 5 www.varsitylearning.com 4
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