53 7.2 Factoring by Grouping
First thing to do when factoring is to factor out the GCF. This GCF is often a monomial, like in the problem 
where the GCF is the monomial 
, so you would have 
. However, a GCF does not have to be a monomial; it could be a binomial. Consider the following two examples.
Example 7.2.1
Find and factor out the GCF for 
.
By observation, one can see that both have 
in common.
This means that 
.
Example 7.2.2
Find and factor out the GCF for 
.
Both have 
as a common factor.
This means that if you factor out , you are left with 
.
The factored polynomial is written as 
.
In the same way as factoring out a GCF from a binomial, there is a process known as grouping to factor out common binomials from a polynomial containing four terms.
Find and factor out the GCF for 
.
To do this, first split the polynomial into two binomials.
becomes 
and 
.
Now find the common factor from each binomial.
has a common factor of 
and becomes 
.
has a common factor of 2 and becomes 
.
This means that 
.
can be factored as 
.
Questions
Factor the following polynomials.
