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 a 3 +b 3 or a 3 –b 3, you can factor by using the following patterns. Note: The first and last term are cubed and these are binomials.

3. Example Factor x 3 + 343. Note: This is a binomial. Are the first and last terms cubed? SOP x 3 + 343 = (x) 3 + (7) 3 = ( + )( - + )x7x2x2 7x49

4. Example Factor 64a 4 – 27a = a(64a 3 – 27) Note: Binomial. Is the first and last terms cubes? = a( (4a) 3 – (3) 3 ) Note: = a( - )( + + )4a316a 2 12a9 S O P

5. Factor by Grouping Some four term polynomials can be factor by grouping. Example. Factor 3x 3 + 7x 2 +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 3x 3 + 7x 2 -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.