Question 20 on the MAT0020/24C Beginning Algebra State Exam

Factoring a Polynomial:  Difference of Two Squares

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 difference of two square because there are only 2 terms, there is a subtraction sign in the middle, and the front and back terms can be square rooted.

Make sure the expression can be factored by pulling out the Greatest Common Factor first.  If you can factor by pulling out the GCF, that should be completed first.

The first step is to take the square root of the front term is: 

Then take the square root of the back term is:

The solution is: 

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

Practice Problems for Question 20

Factoring a Polynomial:  Difference of Two Squares

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.  d                 3.  c                 4.  b