EX 2 3 EX 2x X 5 , 15 X 5 - Tripod
Algebra IIName:Worksheet #1Factoring Polynomials: GCF and Factoring by GroupingFind the GCF (greatest common factor) of the expressions.EX5 x 2 y 2 , 30 x 3 y(The GCF is 5 x 2 y)The GCF is (2 x x 5 , 15 x 5EX(x 5)) EXERCISES: Find the GCF of the expressions.1.x2 , x3.2.t4 , t72 x 2 , 12 x4.36 x 4 , 18 x 3 5.u 2 v , u 3v 2 6.x 6 y 4 , xy 7.9 y 8 z 4 , 12 y 5 z 4 8. 15 x 6 y 3 , 45 xy 3 9.14 x 2 , 1 , 7 x 4 10.5 y 4 , 10 x 2 y 2 11.28 a 4 b 2 , 14 a 3 , 42 a 2 b 5 12.16 x 2 y , 12 xy 2 , 36 x 2 13.2 x 3 , 3 x 3() (x (7 x 5) , 7 x) 14.14 x 5 , 3 x x 5 5 16.x 4, y x 4 15.6 ()(Solutions:1. x 23. 2 x5. u 2 v7. 3 y 5 z 49. 1 11. 14 a 213.(x 3)(15.(7x 5) Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping))
Algebra IIName:Factor out the GCF from each expression using the DISTRIBUTIVE PROPERTY(backwards).12 x 3 y 2 36 x 2 y 6 xEX ' 6 x & 2 x 3 y 2 6 xy 1 )%(GCF is 6 x , EXERCISES:Factor out the GCF from each expression using the distributive property.3x 317.6 x 368 t 1625 x 1019.21. 23. 25. 27. x2 x29.25u 2 14u31.2x 4 6x 333.27 x 2 9 y 212 x 2 2 x10 r 3 35 r100 75 z 50 z 29 x 4 6 x 3 18 x 216 a 3 b 3 24 a 4 b 3 49.10 ab 10 a 2 b 51.15 m 4 n 3 25 m 7 n 30 m 4 n 8 5u 3 5u 2 5u 36 t 4 24 t 29 z 6 27 z 412 x 2 5 x 312 u 7 9u 5 144 a 8 24 a 69 3 y 15 y 242 t 3 21 t 2 744.32 a 5 2 a 3 6 a46.11 y 3 22 y 2 11 y9 x 4 y 24 x 2 y 48. Solutions:)x3 x 38.40. 42.12 x 2 16 x 8(8 x 3 12 30.32. 34. 36. 43.45. 47. 4 x 284u 1214 y 720.22. 24. 26. 28.24 y 2 18 35.37. 39. 41.5y 518.50.21 x 2 y 5 35 x 6 y52.4 xy 8 x 2 y 24 x 4 y 5 ()()(()17. 3 x 1 19. 6 x 6 21. 8 t 2 23. 5 5x 2 25. 6 4y())((2))()( 3 27. x x 1 29. u 25u 14 ())(31. 2 x 3 x 3 33. 9 3x 2 y 2 35. 2 x 6 x 1 37. 5r 2r 2 7 39. 4 3x 2 4 x 2 41. 25 4 3z 2z 2(()())(43. 3x 2 3x 2 2 x 6 45. 5u u 2 u 1 47. 8a 3b 3 2 3a 49. 10ab 1 a 51. 5m 4n 3n 2 5m 3 6n 7()()))Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping
Algebra IIEXName:Factor out a positive GCF from this expression.(15 5 x 5 3 x)Factor out a negative GCF from this expression. ( 5 ( x15 5 x 5 3 x 3))BOTH ARE CORRECT! EXERCISES:Factor out the GCF from each expression using the distributive property.Factor each TWICE 1st: Factor out a POSITIVE GCF.2nd: Factor out a NEGATIVE GCF.53.5 10 x54.3 6x55. 10 x 300056. 3 x 2 4 ** 57. x 2 5 x 10 ** 58. 4 x 2 8 x 20 59.4 12 x 2 x 2 60.8 4 x 12 x 2 ** The only positive common factor is one. For this problem, just do the the 2nd part by factoring out a negative one. Solutions:()(53. 5 1 2 x , 5 2 x 1)()(55. 10 x 300 , 10 x 300)#&#&#&57. 1 % x 2 5 x 10 ( 59. 2 % 2 6 x x 2 ( , 2 % x 2 6 x 2 ( ' ' ' Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping
Algebra IIName:Factor out the common binomial factor.x 2 3x 1 3 3x 1(EX()#& 3 x 1 % x 2 3( '( EX) )()(7x x 3 4 3 x ())Factor out a negativeone to make thisbinomial x 3 .( 7x x 3 4 x 3 (x)( 3 7x 4)()) EXERCISES: Factor out the common binomial factor from each expression using thedistributive property.61.63. 65. 67.() ()y ( q 5 ) 10 ( q 5 )x 3 (y 4 ) y (y 4 )(a b ) (a b ) a (a b )x x 3 5 x 368. Solutions:61. ( x 3 ) ( x 5 )63.(q 5 ) (y 10)65.(y#& 4 % x 3 y ( 67. '))a2 b 2 b b 2 (64.66. )x x 6 3 x 6 (62.() ()x 3 ( x 2 ) 6( x 2 )y 2 ( x y ) 4 (y x )(a b ) (2 a b ) Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping
Algebra IIName:Factoring by Grouping This is a strategy that we can use to factor polynomials that have FOUR terms. This strategy has three steps:(1)Draw parentheses to make TWO groups(2)Factor out the GCF from each of the two groups(3)Factor out the common binomial factor (if there is one).Use factoring by grouping to factor these polynomials.EX( ax 2 x ) ( 2 a 4 )x (a 2 ) 2 (a 2 )(a 2 ) ( x 2 ) ax 2 x 2 a 4EXERCISES:Factor by grouping.69.t 3 3t 2 2 t 670.x 3 6 x 2 2 x 1271.16 x 3 8 x 2 2 x 172.4u 3 2 u 2 6u 3 73.x 3 3x x 2 3 74.x 3 7 x 3 x 2 21 75.3 x 2 x 3 18 6 x 76.5 x 2 10 x 3 4 8 x 77.ky 2 4 ky 2 y 8 78.ay 2 3 ay 3 y 9 79.3 a ab 3 c bc 80.x 2 2 x xy 2 y 81.h 2 hk hr kr 82.p 3 2 p 2 4p 8 83.p 2 2 pq pr 2 qr 84.3 hk 2 k 12 h 8 Solutions:69.79.( t 3 ) #% t 2 2 &(' 71. ( 2 x 1 ) #% 8 x 2 1 &(' 73. ( x 1 ) #% x 2( a c ) ( 3 b ) 81. ( h k ) ( h r ) 83. ( p 2 q ) ( p r )& 3 ( 75.' ( x 3 ) #% x 2& 6 ( 77.'(y)( 4 ky 2 Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping)
Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping Find the GCF (greatest common factor) of the expressions. EX 5x2y2, 30x3y EX 2x(x 5), 15(x 5) The GCF is 5x2y The GCF is (x 5) EXERCISES: Find the GCF of the expressions. 1. x2, x6 2. 2 t4 .
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