1. Section 5.3 – Solving Polynomial Equations Students will be able to: Solve polynomial equations by factoring Solve polynomial equations by graphing Lesson Vocabulary Sum of Cubes Difference of Cubes

2. Section 5.3 – Solving Polynomial Equations To solve a polynomial equations by factoring: 1.Write the equation in the form P(x) = 0 for some polynomial function P. 2.Factor P(x). Use the Zero Product Property to find the roots.

3. Section 5.3 – Solving Polynomial Equations Problem 1: What are the real or imaginary solutions of each polynomial equation? 2x 3 – 5x 2 = 3x

4. Section 5.3 – Solving Polynomial Equations Problem 1b: What are the real or imaginary solutions of each polynomial equation? 3x 4 + 12x 2 = 6x 3

5. Section 5.3 – Solving Polynomial Equations Problem 1c: What are the real or imaginary solutions of each polynomial equation? (x 2 – 1)(x 2 + 4) = 0

6. Section 5.3 – Solving Polynomial Equations Problem 1d: What are the real or imaginary solutions of each polynomial equation? x 5 + 4x 3 = 5x 4 – 2x 3

7. Section 5.3 – Solving Polynomial Equations

10. Problem 2: What are the real or imaginary solutions of each polynomial equation? x 4 – 3x 2 = 4

11. Section 5.3 – Solving Polynomial Equations Problem 2b: What are the real or imaginary solutions of each polynomial equation? x 3 = 1

12. Section 5.3 – Solving Polynomial Equations Problem 2c: What are the real or imaginary solutions of each polynomial equation? x 4 = 16

13. Section 5.3 – Solving Polynomial Equations Problem 2c: What are the real or imaginary solutions of each polynomial equation? x 3 = 8x – 2x 2

14. Section 5.3 – Solving Polynomial Equations Problem 2d: What are the real or imaginary solutions of each polynomial equation? x(x 2 + 8) = 8(x +1)

15. Section 5.3 – Solving Polynomial Equations While factoring is an effective way to solve a polynomial equation, you can also find the REAL roots quickly by using a graphing calculator. Problem 3: What are the real solutions of the equation x 3 + 5 = 4x 2 + x?

16. Section 5.3 – Solving Polynomial Equations Problem 3b: What are the real solutions of the equation x 3 + x 2 = x – 1?

17. Section 5.3 – Solving Polynomial Equations Problem 4: Close friends Stacy, Una, and Amir were all born on July 4. Stacy is one year younger than Una. Una is 2 years younger than Amir. On July 4, 2010, the product of their ages was 2300 more than the sum of their ages. How old was each friend on that day?

18. Section 5.3 – Solving Polynomial Equations Problem 5: The width of a box is 2 m less than the length. The height is 1 m less than the length. The volume is 60 cubic m. What is the length of the box?

19. Section 5.3 – Solving Polynomial Equations Problem 6: The product of three consecutive integers is 210. What are the numbers?

20. Section 5.3 – Solving Polynomial Equations Problem 7: A student claims that 1, 2, 3, and 4 are all zeros of a cubic polynomial function. Explain why the student must be mistaken.