Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 27: The GCF and Factoring by Grouping
Answer/Discussion
to 1a
The largest monomial that we can factor out of
each term is . 

*Divide out of every term of the poly. 
Answer/Discussion
to 1b
The largest monomial that we can factor out of
each term is . 

*Divide out of every term of the poly. 
Answer/Discussion
to 1c
Note how there is not a GCF for ALL the terms.
So let's go ahead and factor this by grouping. 
Step 1: Group the first two terms together and then
the last two terms together. 
Step 2: Factor out a GCF from each separate binomial
AND
Step 3: Factor out the common binomial. 

*Factor out an a squared
from the 1st ( )
*Factor out a 5 from the 2nd ( )
*Divide (a  2)
out of both parts 
Answer/Discussion
to 1d
Note how there is not a GCF for ALL the terms.
So let's go ahead and factor this by grouping. 
Step 1: Group the first two terms together and then
the last two terms together. 
Step 2: Factor out a GCF from each separate binomial
AND
Step 3: Factor out the common binomial. 

*Factor out an a 3x from the 1st ( )
*Factor out a 2 from the 2nd ( )
*Divide (y + 7)
out of both parts 
Last revised on July 15, 2011 by Kim Seward.
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