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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.