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Chapter 5.2 Factoring by Grouping

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3y (2x – 7)( ) (2x – 7) (2x – 7) – 8 3y 1. Factor. GCF = (2x – 7) Find the GCF. Divide each term by the GCF. (2x – 7) – 8 (2x – 7)

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Factoring by grouping (4 terms). 1. See if there is a GCF of all terms. 2. The product of the 1 st and 4 th terms must be equal to the product of the 2 nd and 3 rd terms. If not rewrite them. 3. Factor the GCF from the 1 st and 2 nd terms. 4. Factor the GCF from the 3 rd and 4 th terms so that the expressions in both parentheses are the same. 5. Factor one more time, the expression from the parentheses.

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6x 2 (2x – 5)( ) 3x 2 3x + 2 1. GCF = -60x 2 -60x 2 3x( ) 2x – 5 + 2( ) 2x – 5 (2x – 5) (2x – 5) – 15x+ 4x– 10 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? YES, now factor. 2. Factor. 1 3. The GCF = 3x 4. The GCF = 2 5. The GCF = (2x – 5)

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ax (x + 2)( ) a 4b a + 4b 1. GCF = 8abx 8abx a( ) x + 2 + 4b( ) x + 2 (x + 2) (x + 2) + 2a+ 4bx+ 8b 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? YES, now factor. 3. Factor. 1 3. The GCF = a 4. The GCF = 4b 5. The GCF = (x + 2)

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6a 2 (3a + 5b)( ) 2a c 2a + c 1. GCF = 18a 3 c 50ab 2 c 2a( ) 3a + 5b + c( ) 3a + 5b (3a + 5b) (3a + 5b) + 5bc+ 10ab+ 3ac 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? No, now rewrite it and check. 4. Factor. 1 3. The GCF = 2a 4. The GCF = c 5. The GCF = (3a + 5b) 6a 2 + 10ab+ 3ac+ 5bc 30a 2 bc 30a 2 bc

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6xy (3y + 7)( ) 2x -5 2x – 5 1. GCF = -210xy -210xy 2x( ) 3y + 7 – 5( ) 3y + 7 (3y + 7) (3y + 7) + 14x– 15y– 35 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? YES, now factor. 5. Factor. 1 3. The GCF = 2x 4. The GCF = -5 5. The GCF = (3y + 7)

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3x (x + 2y)( ) 3 -5a 3 – 5a 1. GCF = -30axy -30axy 3( ) x + 2y – 5a( ) x + 2y (x + 2y) (x + 2y) + 6y– 5ax– 10ay 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? YES, now factor. 6. Factor. 1 3. The GCF = 3 4. The GCF = -5a 5. The GCF = (x + 2y)

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10ad (5a – 3b)( ) 2d -9c 2d – 9c 1. GCF = -450a 2 cd -162b 2 cd 2d( ) 5a – 3b – 9c( ) 5a – 3b (5a – 3b) (5a – 3b) + 27bc– 6bd– 45ac 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? No, now rewrite it and check. 7. Factor. 1 3. The GCF = 2d 4. The GCF = -9c 5. The GCF = (5a – 3b) 10ad– 6bd– 45ac+ 27bc 270abcd 270abcd

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Chapter 5.2 Factoring by Grouping

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