3 Title

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.

 *Two groups of two terms

 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.

 *Two groups of two terms

 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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