1. 6.4 Factoring and Solving Polynomial Equations

2. Factoring Sum or Difference of Cubes
If you have as sum or difference of cubes such as a3 +b3 or a3 –b3, you can factor by using the following patterns.
Note: The first and last term are cubed and these are binomials.

3. Example
Factor x
Note: This is a binomial. Are the first and last terms cubed? S O P
x = (x)3 + (7)3
= ( )( ) x 7 x2 7x 49

4. Example Factor 64a4 – 27a = a(64a3 – 27)
Note: Binomial. Is the first and last terms cubes?
= a( (4a)3 – (3)3)
Note:
= a( )( ) 4a 3
16a2
12a 9
S O P

5. Factor by Grouping
Some four term polynomials can be factor by grouping.
Example Factor 3x3 + 7x2 +12x + 28
Step 1 Pair the terms.
Step 2 Factor out common factor from each pair.
Identical factors
Step 3 Factor out common factor from each term.

6. Example Factor 3x3 + 7x2 -12x - 28 Step 1
Note: Subtraction is the same as adding a negative
Step 2
Step 3
Note: This factor can be further factored

7. Solving Polynomial Equations
Solve
Set equation equal to zero.
Factor.
Set each factor equal to zero and solve.