1. Solving
Special Cases

2. List all the ways we have discussed to find the zeros of a polynomial:
Look at the graph – observe the x-intercepts
Factor – set each factor equal to zero and solve
Quadratic formula – works only for quadratics
Square roots – again only works with quadratics

3. # of solutions
A polynomial equation has the same number of solutions as its degree! How many solutions does each poly have? 1) 4x3 - 4x + 4 = 0 2) 3x2 + x + 3 = 0 3) 5x4 + 7x - 1 = 0

4. Let’s list all of the ways we have found to solve:

5. Solve: x3 – x2 – 2x – 12 = 0 Can we factor? Quadratic Formula?
Complete the square?
So…. Only way to solve is by graphing.

6. Graph x3 – x2 – 2x – 12 = 0 How many x-intercepts do you see
Graph x3 – x2 – 2x – 12 = 0 How many x-intercepts do you see? How many should there be? What does that mean?

7. How do we find the other solutions?
x3 – x2 – 2x – 12 = 0 1) Use the one real solution and turn it into a factor. 2) Use long division to divide. 3) Solve the remaining quadratic by one of our methods.

8. Try one!
2x3 + 9x = 0

9. Solve
4x3 – 8x2 + 4x = 0

10. Solve
x3 – 8 = 0

11. Solve
x3 – 64 = 0

12. Solve
x = 0

13. Solve
x4 – 2x2 – 8 = 0

14. Solve
x4 + 7x2 + 6 = 0

15. Solve
x4 – 3x2 – 10 = 0