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1.2 Binomial Common Factors: Worked Examples

Example 1. Factor out the GCF:  

The expression has two terms. The binomial (x - 1) is common to both terms.

The GCF is the binomial with the lesser power:  

Divide all of the terms by the GCF:  

Multiply the two factors together:  

Example 2. Factor out the GCF:  

The expression has two terms. The binomial (x + 3) is common to both terms. The

GCF is the binomial with the lesser power:  

Divide all of the terms by the GCF:  

Multiply the two factors together:  

Example 3. Factor out the common term with the lesser power:  

The expression has two terms. The binomial (2x - 1) is common to both. We use a

factor of this binomial to the lesser power:  

Divide all of the terms by :  

Multiply the two factors together:  

Example 4. Factor out the common term with the lesser power and…any other common

factors:  

The expression has two terms. The two terms enjoy a common factor of 2 and a

factor of . Additionally, the binomial (3 x) is common to both. We use a factor of

the binomial to the lesser power  

together with the factors .

Divide all of the terms by :  

Multiply the two factors together:  

Example 5. Factor out the GCF:  

The expression has two terms. The GCF is  

Divide all of the terms by the GCF:  

Multiply the factors together:  

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