1. 6.4: Factoring and Solving Polynomial Equations Objectives: Students will be able to… Factor the sum and difference of 2 cubes Factor by grouping Solve a polynomial equation by factoring

2. Complete the table: n123456789101112 n3n3

3. Factoring Sum and Difference of Cubes: Sum of 2 Cubes: a 3 + b 3 = ( a + b ) (a 2 – ab + b 2 ) EX: x 3 + 64 = (x + 4)(x 2 – 4x + 16) Difference of 2 Cubes: a 3 – b 3 = (a –b)(a 2 + ab + b 2 ) EX: (27x 3 – 8) = (3x – 2)(9x 2 + 6x + 4)

4. Examples: Factor

5. Factor:

6. Factor by Grouping Use on some polynomials Group pairs of terms that have a common monomial factor ra + rb + sa + sb = (ra + rb) +(sa + sb) = r (a + b) + s(a +b) = (r +s)(a +b)

7. Factor:

10. Solving Polynomial Equations You can use the Zero Product Property to solve higher-degree polynomials. 1.) Set Polynomial equal to 0 2.) Factor Polynomial (We have so many methods to choose from now !!) 3.) Set each factor = 0 and solve.

11. Find all real number solutions. 2y 5 = 18y

12. Find all real number solutions 5x 3 + 10x 2 – x – 2= 0

13. Find all real number solutions. x 3 - 27 = 0 Graph the polynomial. What do you notice?

14. Extra Examples: Find real # solutions.

15. Find real # solutions, then graph. What do you notice? 4x 4 + 20x 2 = -25

16. You are building a bin to hold cedar mulch for your garden. The bin will hold 162 ft 3 of mulch. The dimensions of the bin are x ft. high, by 5x -6 ft by 5x -9 ft. How tall is the bin?