Intermediate Algebra Tutorial 27


Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 27: The GCF and Factoring by Grouping

WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 27: The GCF and Factoring by Grouping


 

checkAnswer/Discussion to 1a

problem 1a

The largest monomial that we can factor out of each term is ad1a1.
 

ad1a2

*Divide ad1a1 out of every term of the poly.

 
(return to problem 1a)

 


 

checkAnswer/Discussion to 1b

problem 1b

The largest monomial that we can factor out of each term is ad1b1.
 

ad1b2

*Divide ad1b1 out of every term of the poly.

 
(return to problem 1b)

 


 

checkAnswer/Discussion to 1c

problem 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.

 
ad1c1

*Two groups of two terms 

 
Step 2: Factor out a GCF from each separate binomial
AND
Step 3: Factor out the common binomial.

 
ad1c2
*Factor out an a squared from the 1st (  )
*Factor out a 5 from the 2nd (  ) 

*Divide (a - 2) out of both parts
 

(return to problem 1c)

 


 

checkAnswer/Discussion to 1d

problem 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.

 
ad1d1

*Two groups of two terms 

 
Step 2: Factor out a GCF from each separate binomial
AND
Step 3: Factor out the common binomial.

 
ad1d2
*Factor out an a 3x from the 1st (  )
*Factor out a 2 from the 2nd (  ) 

*Divide (y + 7) out of both parts
 

(return to problem 1d)

 

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Last revised on July 15, 2011 by Kim Seward.
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