Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F5: The Difference of Two Squares and Perfect Square Trinomials| VERSION B Factor the following. 1.
2.
6.
12𝑦 ! − 27 7.
50𝑥 ! − 8𝑥 8.
𝑦 ! − 𝑏 ! 9.
625𝑦 ! − 81 𝑥 ! − 36 𝑥 ! − 81 3.
3𝑥 ! − 75 4.
4𝑥 ! − 25 5.
4𝑟 ! − 9𝑦 ! 10. 𝑥 ! − 10𝑥 + 25 www.varsitylearning.com 1 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F5: The Difference of Two Squares and Perfect Square Trinomials| VERSION B 11. 𝑥 ! + 8𝑥 + 16 Factor the following by first factoring out the greatest common factor. 16. 5𝑦 ! − 10𝑦 + 5 12. 𝑦 ! − 6𝑦 + 9 17. 5𝑥 ! − 50𝑥 + 125 13. 16𝑥 ! − 8𝑥 + 1 Factor by grouping the first three terms together. 18. 𝑟 ! + 10𝑟 + 25 − 𝑏 ! 14. 16𝑎 ! + 40𝑎 + 25 15. 16𝑟 ! + 8𝑟𝑦 + 𝑦 ! 19. 𝑦 ! + 2𝑦𝑟 + 𝑟 ! − 9 20. Find the value of 𝑎 so that the polynomial 𝑎𝑥 ! − 8𝑥 + 1 factors to 4𝑥 − 1 ! . www.varsitylearning.com 2 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F5: The Difference of Two Squares and Perfect Square Trinomials| VERSION B Factor the following. 1.
2.
6.
12𝑦 ! − 27 3 2𝑦 − 3 2𝑦 + 3 7.
50𝑥 ! − 8𝑥 2𝑥 ⋅ 5𝑥 − 2 5𝑥 + 2 8.
𝑦 ! − 𝑏 ! 𝑦 − 𝑏 𝑦 + 𝑏 9.
625𝑦 ! − 81 5𝑦 − 3 5𝑦 + 3 25𝑦 ! + 9 𝑥 ! − 36 𝑥 − 6 𝑥 + 6 𝑥 ! − 81 𝑥 − 9 𝑥 + 9 3.
3𝑥 ! − 75 3 𝑥 − 5 𝑥 + 5 4.
4𝑥 ! − 25 2𝑥 − 5 2𝑥 + 5 5.
4𝑟 ! − 9𝑦 ! 2𝑟 − 3𝑦 2𝑟 + 3𝑦 10. 𝑥 ! − 10𝑥 + 25 𝑥 − 5 ! www.varsitylearning.com 3 Name: _______________________________________ Algebra 1: Factoring Polynomials
Topic F5: The Difference of Two Squares and Perfect Square Trinomials| VERSION B 11. 𝑥 ! + 8𝑥 + 16 𝑥 + 4 ! Factor the following by first factoring out the greatest common factor. 16. 5𝑦 ! − 10𝑦 + 5 5 𝑦 − 1 ! 12. 𝑦 ! − 6𝑦 + 9 𝑦 − 3 ! 17. 5𝑥 ! − 50𝑥 + 125 5(𝑥 − 5)! 13. 16𝑥 ! − 8𝑥 + 1 4𝑥 − 1 ! Factor by grouping the first three terms together. 18. 𝑟 ! + 10𝑟 + 25 − 𝑏 ! 𝑟 + 5 + 𝑏 𝑟 + 5 − 𝑏 14. 16𝑎 ! + 40𝑎 + 25 4𝑎 + 5 ! 15. 16𝑟 ! + 8𝑟𝑦 + 𝑦 ! 4𝑟 + 𝑦 ! 19. 𝑦 ! + 2𝑦𝑟 + 𝑟 ! − 9 𝑦 + 𝑟 − 3 𝑦 + 𝑟 + 3 20. Find the value of 𝑎 so that the polynomial 𝑎𝑥 ! − 8𝑥 + 1 factors to 4𝑥 − 1 ! . 16 www.varsitylearning.com 4