Question 19 on the MAT0020/24C Beginning Algebra State Exam

Factoring a Polynomial:  Greatest Common Factor (GCF)

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 factoring by pulling out the Greatest Common Factor.

To determine the GCF of the coefficients we look at the prime factors of the coefficients:

The Greatest Common Factor of the coefficients is:  2

To determine the Greatest Common Factor of the variables, we look for the most of each variable in each term.  All of the terms must have the variable for it to be factored out.  It will be the smallest exponent as long as all terms have the variable.

The Greatest Common Factor for the variable y is: 

The Greatest Common Factor for the variable s is: 

The Greatest Common Factor is: 

If we factor out  from each term, we need to show what is remaining.

If we divide each term by , that will give the remaining.

The solution is: 

Note: This solution can be checked by using the distributive property but be sure to

pull out the greatest common factor.

Practice Problems for Question 19

Factoring a Polynomial:  Greatest Common Factor (GCF)

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. b                  2.  b                 3.  d                 4.  b