Question 21 on the MAT0020/24C Beginning Algebra State Exam

Factoring a Polynomial:  By Grouping

Solution:  Factor completely: 

The first step to factor this problem is to identify which method can be used to factor.  In this case the factoring method is grouping because there are 4 terms, the Greatest Common Factor can not be factored out of all 4 terms, but we can group terms and then factor out a Greatest Common Factor.

The next step is to group terms that have similar factors.

The next step is to factor out similar terms from each group.

The next step is to notice that both groups now have a common factor of (r + k).

Factor out the (r + k) from both group and show what remains.

The solution is: 

Note:  This solution can be checked by simplifying through FOIL.

Practice Problems for Question 21

Factoring a Polynomial:  By Grouping

Solutions Below

1.  Factor:       

a.           b.           c.           d. 

2.  Factor:       

a.           b.           c.            d. 

3.  Factor:       

a.        b.      c.      d. 

4.  Factor:       

a.         b.         c.           d. 

Solutions:

1. a                  2.  c                      3.  c                        4.  a