Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E3: Greatest Common Factor | VERSION A Factor the following by taking out the greatest common factor. 1.
2.
3.
6.
25𝑎𝑏 ! 𝑐 ! + 15𝑎 ! 𝑐 ! − 25𝑎𝑐 ! 7.
8𝑎 ! 𝑎 + 𝑏
8.
5𝑥 ! 𝑥 − 5 − 6𝑥 𝑥 − 5 + 3 𝑥 − 5 7𝑎 ! − 5𝑎 ! !
+ 10𝑏 ! 𝑎 + 𝑏 ! 42𝑥 ! 𝑦 − 7𝑥𝑦 ! 9𝑏 ! + 18𝑏 ! + 21𝑏 Factor the following by grouping. 4.
−60𝑥 ! 𝑦 ! + 108𝑥 ! 𝑦 ! + 132𝑥 ! 𝑦 ! 5.
4𝑥 𝑎 − 𝑏 + 3𝑦 𝑎 − 𝑏 9.
2𝑥𝑦 + 2𝑦 − 5𝑎𝑥 − 5𝑎 10. 3𝑥𝑦 + 12𝑦 + 𝑎𝑥 + 4𝑎 www.varsitylearning.com 1 Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E3: Greatest Common Factor | VERSION A 11. 𝑥 ! 𝑦 − 2𝑥 + 4𝑥𝑦 − 8 = 16. 𝑎 ! − 2𝑎 ! + 9𝑎 − 18 = 12. 3𝑥𝑦 ! + 6𝑦 ! − 2𝑥 − 4 = 17. 3𝑥 ! − 4𝑥 ! + 27𝑥 − 36 = 13. 𝑎 ! + 𝑥𝑎 − 𝑦𝑎 − 𝑥𝑦 = 18. 4𝑎 ! − 20𝑎 ! + 𝑎 − 5 = 14. 𝑥𝑦 + 2𝑥 + 3𝑦 + 6 = 19. 4𝑥 ! + 12𝑥 ! + 𝑥 + 3 = 15. 𝑎 ! 𝑏 ! − 2𝑎 ! + 𝑏 ! − 2 = 20. The greatest common factor of the binomial 4𝑥 + 4 is 4. The greatest common factor of the binomial 4𝑥 − 12 is 4. What is the greatest common factor of their product, 4𝑥 + 4 4𝑥 − 12 , when it has been multiplied out? www.varsitylearning.com 2 Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E3: Greatest Common Factor | VERSION A Factor the following by taking out the greatest common factor. 1.
6.
25𝑎𝑏 ! 𝑐 ! + 15𝑎 ! 𝑐 ! − 25𝑎𝑐 ! = 5𝑎𝑐 ! 5𝑏 ! 𝑐 + 3𝑎 ! 𝑐 − 5 7.
8𝑎 ! 𝑎 + 𝑏 ! + 10𝑏 ! 𝑎 + 𝑏
2 𝑎 + 𝑏 ! 4𝑎 ! + 5𝑏 ! 8.
5𝑥 ! 𝑥 − 5 − 6𝑥 𝑥 − 5 + 3 𝑥 − 5 = 𝑥 − 5 5𝑥 ! − 6𝑥 + 3 7𝑎 ! − 5𝑎 ! = 𝑎 ! 7𝑎 − 5 2.
42𝑥 ! 𝑦 − 7𝑥𝑦 ! = 7𝑥𝑦 ⋅ 6𝑥 − 𝑦 3.
9𝑏 ! + 18𝑏 ! + 21𝑏 = 3𝑏 ⋅ 3𝑏 ! + 6𝑏 + 7 4.
−60𝑥 ! 𝑦 ! + 108𝑥 ! 𝑦 ! + 132𝑥 ! 𝑦 ! = 12𝑥 ! 𝑦 ! −5𝑥 + 9𝑦 + 11𝑥𝑦 = Factor the following by grouping. 9.
5.
!
2𝑥𝑦 + 2𝑦 − 5𝑎𝑥 − 5𝑎 = 𝑥 + 1 2𝑦 − 5𝑎 4𝑥 𝑎 − 𝑏 + 3𝑦 𝑎 − 𝑏 = 𝑎 − 𝑏 4𝑥 + 3𝑦 10. 3𝑥𝑦 + 12𝑦 + 𝑎𝑥 + 4𝑎 = 𝑥 + 4 3𝑦 + 𝑎 www.varsitylearning.com 3 Algebra 2: Exponents and Polynomials
Name: _________________________________________ Topic E3: Greatest Common Factor | VERSION A 11. 𝑥 ! 𝑦 − 2𝑥 + 4𝑥𝑦 − 8 = 𝑥𝑦 − 2 𝑥 + 4 16. 𝑎 ! − 2𝑎 ! + 9𝑎 − 18 = 𝑎 − 2 𝑎 ! + 9 12. 3𝑥𝑦 ! + 6𝑦 ! − 2𝑥 − 4 = 𝑥 + 2 3𝑦 ! − 2 17. 3𝑥 ! − 4𝑥 ! + 27𝑥 − 36 = 3𝑥 − 4 𝑥 ! + 9 13. 𝑎 ! + 𝑥𝑎 − 𝑦𝑎 − 𝑥𝑦 = 𝑎 + 𝑥 𝑎 − 𝑦 18. 4𝑎 ! − 20𝑎 ! + 𝑎 − 5 = 𝑎 − 5 4𝑎 ! + 1 14. 𝑥𝑦 + 2𝑥 + 3𝑦 + 6 = 𝑦 + 2 𝑥 + 3 19. 4𝑥 ! + 12𝑥 ! + 𝑥 + 3 = (𝑥 + 3)(4𝑥 ! + 1) 15. 𝑎 ! 𝑏 ! − 2𝑎 ! + 𝑏 ! − 2 = 𝑏 ! − 2 𝑎 ! + 1 20. The greatest common factor of the binomial 4𝑥 + 4 is 4. The greatest common factor of the binomial 4𝑥 − 12 is 4. What is the greatest common factor of their product, 4𝑥 + 4 4𝑥 − 12 , when it has been multiplied out? 16 www.varsitylearning.com 4