55 2.1 Factoring out the GCF and Factoring by Grouping CHAPTER 2 POLYNOMIAL FACTORING 2.1 Factoring out the GCF and Factoring by Grouping Factor the given polynomial. 1. 5 5 x y + 2. 6 6 a b - 3. 3 6 xy x - 4. 15 6 a ab - 5. 2 4 x x - 6. 2 18 y y - 7. 2 8n n + 8. 2 12 16 x x + 9. 3 2 8 2 a a - 10. 3 4 9 36 b b - 11. 2 12 20 xy xy + 12. 2 3 3 2 35 55 ab ab - + 13. 2 2 18 9 27 mn mn mn - + 14. 2 5 3 3 2 3 64 40 8 xy xy xy + + 15. 2 3 2 2 2 25 15 5 a bc ab c abc + - 16. 4 3 2 2 3 2 2 4 24 28 40 xyz xyz x yz - - 17. ( ) ( ) 2 5 ax y bx y + + + 18. ( ) ( ) 9 7 na b pa b - - - 19. ( ) ( ) 6 9 7 9 yx wx + + + 20. ( ) ( ) 3 8 8 8 xy y - - + - 21. ( ) ( ) 15 12 16 12 n m p m - + - 22. ( ) ( ) 2 10 15 10 xy a a + + + 23. ( ) ( ) 6 12 6 xy y - + - 24. ( ) ( ) 2 3 5 3 y x zx - + - 25. ( ) ( ) 8 2 10 2 m c d nd c - + - 26. ( ) ( ) 5 3 4 15 4 3 a x y y x - - -
32
Embed
2.1 Factoring out the GCF and Factoring by Grouping · 55 2.1 Factoring out the GCF and Factoring by Grouping CHAPTER 2 POLYNOMIAL FACTORING 2.1 Factoring out the GCF and Factoring
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
55
2.1 Factoring out the GCF and Factoring by Grouping
CHAPTER 2 POLYNOMIAL FACTORING
2.1 Factoring out the GCF and Factoring by Grouping Factor the given polynomial.
1. 5 5x y+ 2. 6 6a b−
3. 3 6xy x− 4. 15 6a ab−
5. 24x x− 6. 218y y−
7. 28n n+ 8. 212 16x x+
9. 3 28 2a a− 10. 3 49 36b b−
11. 212 20xy xy+ 12. 2 3 3 235 55a b a b− +
13. 2 218 9 27mn mn m n− + 14. 2 5 3 3 2 364 40 8x y x y x y+ +
15. 2 3 2 2 225 15 5a bc ab c abc+ − 16. 4 3 2 2 3 2 2 424 28 40x y z x y z x yz− −
17. ( ) ( )2 5a x y b x y+ + + 18. ( ) ( )9 7n a b p a b− − −
19. ( ) ( )6 9 7 9y x w x+ + + 20. ( ) ( )3 8 8 8x y y− − + −
21. ( ) ( )15 12 16 12n m p m− + − 22. ( ) ( )2 10 15 10xy a a+ + +
23. ( ) ( )6 12 6x y y− + − 24. ( ) ( )2 3 5 3y x z x− + −
25. ( ) ( )8 2 10 2m c d n d c− + − 26. ( ) ( )5 3 4 15 4 3a x y y x− − −
56
2.1 Factoring out the GCF and Factoring by Grouping
27. ( ) ( )4 2 2 2n ab c m c ab− + − 28. ( ) ( )18 5 27 5a y x b x y− − −
29. ( ) ( )20 3 2 25 2 3w t y t+ − + 30. ( ) ( )8 4 5 16 4 5t x t− − − +
31. ( )( ) ( )( )2 3a x y b x y+ + + + + 32. ( )( ) ( )( )4 8 4 1x y x z− − + − +
33. ( )( ) ( )( )2 1 2 1 1n m n m− + − − + 34. ( )( ) ( )( )2 5 3 6 3x y x y− − − + −
35. ( )( ) ( )( )6 2 3 2 1 3y x w y x w− + + − − + 36. ( )( ) ( )( )4 4a b x y b a x y− − − − −
37. ( )( ) ( )( )2 21 2 2 1 2x x y x x y+ + + + − + + 38. ( )( ) ( )( )2 5 2 5a b c m a b c m− + + + − + + +
39. ( ) ( )2 22 1 1x y y y+ − + 40. ( ) ( )
4 45 2 6 22 3 7 3a c b c+ − +
57
2.1 Factoring out the GCF and Factoring by Grouping
41. 3 3x y ax ay− + − 42. 4 8 5 10a b ac bc+ + +
43. 6 4 15 10ab bc a c− + − 44. 10 5 6 3xy x y+ + +
45. 2 4 4x x xy y− + − 46. 3 23 3y y y+ + +
47. 2 5 5a ab a b− − + 48. 3 22 5 2 5x x x− + −
49. 2 6 6n n nx x+ − − 50. 3 23 6 4 8a a a+ − −
58
2.1 Factoring out the GCF and Factoring by Grouping
51. 6 12 5 10ax a bx b+ − − 52. 8 80 9 90my m ny n− − +
53. 14 16 21 24xy y x− − + 54. 9 27 5 15ab ac b c+ − −
55. 3 34 5 20x y y x− − + 56. 3 3 3 22 5 10a ab b a− − +
57. ax ay bx by x y− + − − + 58. 3 3 3ab b ac c ad d+ − − − −
59. 2 2 1x y x xy x y+ + + + + 60. 2 2 4 4 4 8am an a bm bn b− + + − +
59
2.2 Factoring Quadratic Trinomials
2.2 Factoring Quadratic Trinomials Factor the given polynomial.
1. 2 9 14x x+ + 2. 2 16 60x x+ +
3. 2 12 32y y− + 4. 2 16 63y y− +
5. 2 7 30n n+ − 6. 2 9 10n n+ −
7. 2 11 80a a− − 8. 2 7 60a a− −
9. 2 27 50x x− + 10. 2 9 20x x− +
11. 2 12 36m m+ + 12. 2 16 64m m+ +
13. 2 18 81y y− + 14. 2 20 100y y− +
15. 2 22x xy y− − 16. 2 23 10x xy y+ −
17. 2 22 15a ab b+ − 18. 2 24 12a ab b− −
19. 2 26 9m mn n− + 20. 2 28 16m mn n+ +
60
2.2 Factoring Quadratic Trinomials
21. 22 8 10x x− − 22. 23 21 36x x+ +
23. 25 5 150y y+ − 24. 26 48 90y y− +
25. 2 23 18 15a ab b+ + 26. 2 22 12 14a ab b− −
27. 2 24 32 60m mn n− + 28. 2 23 18 48y yx x+ −
29. 2 25 20 20b ab a+ + 30. 2 22 28 98a ab b− +
31. 22 7 4x x− − 32. 23 14 5x x+ −
33. 26 13 6y y+ + 34. 210 29 10y y− +
61
2.2 Factoring Quadratic Trinomials
35. 28 6 9a a+ − 36. 26 7 20a a− −
37. 210 27 5n n− + 38. 212 4 5n n+ −
39. 26 23 15x x+ + 40. 212 37 21x x+ +
41. 2 210 21 10x xy y− − 42. 2 214 15 9x xy y− −
62
2.2 Factoring Quadratic Trinomials
43. 2 230 37 10a ab b+ + 44. 2 224 41 12a ab b− +
45. 2 218 77 18m mn n+ − 46. 2 256 15 56m mn n− −
47. 2 256 42x xy y+ − 48. 2 242 30x xy y− −
49. 2 272 13 20x xy y+ − 50. 2 220 13 72m mn n− −
63
2.3 Factoring Special Binomials
2.3 Factoring Special Binomials Factor the given polynomial.
1. 2 16x − 2. 2 81x −
3. 2 9y − 4. 2 100y −
5. 225 a− 6. 249 b−
7. 2 36n + 8. 264 m+
9. 24 9y− 10. 216 49x −
11. 2 24 81a b− 12. 2 2100 49c d−
13. 2 216a b+ 14. 2 24 25a b+
15. 2 2
25 4
x y− 16.
2 2
36 49
y x−
17. 2
2
4
ba − 18.
22
9
ab −
19. 2 2
4 25
n m+ 20.
2 2
16 81
c d+
21. 2 24 9
9 25
x y− 22.
2 216 36
81 49
y n−
23. 2 21 1
4 25a b− 24. 2 21 1
36 121n m−
25. 2 29 16
25 49x y− 26. 2 24 36
81 25y x−
64
2.3 Factoring Special Binomials
27. 4 16x − 28. 4 81y −
29. 4 416a b− 30. 4 481 625n m−
31. 4181
16y − 32. 41
1681
x−
33. 4 41 1
81 16a b− 34. 4 416 1
625 256y x−
35. 3 27y + 36. 3 8x −
37. 364 n− 38. 3125 a+
39. 3 38 27n m+ 40. 3 3125 64x y−
41. 3 3
8 27
a b+ 42. 3 31 8
64 27x y−
.
65
2.4 Factoring by Substitution
2.4 Factoring by Substitution Factor the given polynomial.