1. Factoring Polynomials
Lesson 5.4

2. Factoring find a common factor
a) b)
After the greatest common factor has been found, factor the trinomial into 2 binomials, if possible
Notice that
is a difference of squares

3. Factoring a Sum of Two Cubes
                              
The sum of two cubes  has to be exactly in this form to use this rule.
1. When you have the sum of two cubes, you have a product of a binomial and a trinomial.
     
2. The binomial is the sum of the bases that are being cubed.
3. The trinomial is the first base squared, the second term is the opposite of the product of the two bases found, and the third term is the second base squared. 

4. Factor the sum of cubes:
Example 1
First note that there is no GCF to factor out of this polynomial.
This fits the form of  the sum of cubes. 
                      
          
The cube root of
The cube root of 27 = 3

5. Factor the sum of cubes: (GCF first, if needed)
Example 2
5x3 + 40
27x3 + 8
                      
          

6. Factoring a Difference of Two Cubes
                              
The difference of two cubes has to be exactly in this form to use this rule.
1. When you have the difference of two cubes, you have a product of a binomial and a trinomial.
2. The binomial is the difference of the bases that are being cubed.
       
3. The trinomial is the first base squared, the second term is the product of the two bases found, and the third term is the second base squared.

7. Factor the difference of cubes:
Example 3
Factor the difference of cubes:
First note that there is no GCF to factor out of this polynomial.
This fits the form of  the difference of cubes.
                      
The cube root of
The cube root of 8 = 2
           

8. Example 4
Factor
54x3 – 81y3
8x3 – y3