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I. Factor the greatest common factor Recall the distributive property: a⋅bc =a⋅ba⋅c Factoring the greatest common factor is the reverse of the distributive property: a⋅ba⋅c=a⋅bc When looking for the greatest common factor (GCF) of a set of terms, you need to find the GCF of the coefficients and the GCF or the variables. Example: Find the GCF of the terms 18 x 2 y , 30 x 3 y 2 , 42 x 5 y 3 GCF of coefficients: the largest factor that all of the numbers have in common GCF of coefficients (18, 30, 42) is 6 GCF of variables: the variable raised to the lowest power of the variable that is in common. GCF of variable x 2 , x 3 , x 5 is x 2 GCF or variable y , y 2 , y3 is y The GCF of 18 x 2 y , 30 x 3 y 2 , 42 x 5 y 3 is 6 x 2 y Factor out the greatest common factor of 18 x 2 y 30 x 3 y 2− 42 x 5 y 3 From above the greatest common factor is 6 x 2 y 2 3 2 5 3 18 x y30 x y − 42 x y 18 x 2 y 30 x 3 y 2 42 x 5 y 3 2 =6 x y − 6 x2 y 6 x2 y 6x 2 y 3⋅6 x 2 y 5⋅6 x⋅x 2 y⋅y 7⋅6 x 3⋅x 2 y 2⋅y =6 x y − 6 x2 y 6 x2 y 6x2 y 2 3 2 =6 x y 35 x y−7 x y 2 Factor the greatest common factor out of the following expressions. 1. 28x−7 4. 14 x 2−21 x28 2. 25a−15b35c−50d 5. 9 x 2 y27 x y−81y 3. 5 c3 d 475 c 2 d 3 6. 4 x 2 y 3 z12 x y 2 z 16 x y