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# Factoring Out the Opposite of the GCF

The GCF, the greatest common factor, for -6x2 - 4x is 2x, but we can factor out either 2x or its opposite, -2x:

 -6x2 - 4x = 2x( 3x - 2) = 2x(3x + 2)

Example 1

Factoring out the opposite of the GCF

Factor out the GCF, then factor out the opposite of the GCF.

a) 5x - 5y

b) -x2 - 3

c) -x3 + 3x2 - 5x

Solution

 a) 5x - 5y = 5(x - y) Factor out 5. = -5 (-x + y) Factor out -5.
 b) -x2 - 3 = 1(-x2 - 3) The GCF is 1. = -1(x2 + 3) Factor out 1.
 c) -x3 + 3x2 - 5x = x(-x2 + 3x - 5) Factor out x. = -x(x2 - 3x + 5) Factor out -x.