Download I. Factor the greatest common factor Recall the

I. Factor the greatest common factor
Recall the distributive property: a⋅bc =a⋅ba⋅c
Factoring the greatest common factor is the reverse of the distributive property: a⋅ba⋅c=a⋅bc
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 y30 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  35 x y−7 x y 
2

Factor the greatest common factor out of the following expressions.
1.
28x−7
4.
14 x 2−21 x28
2.
25a−15b35c−50d
5.
9 x 2 y27 x y−81y
3.
5 c3 d 475 c 2 d 3
6. 4 x 2 y 3 z12 x y 2 z 16 x y