2. 7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each. functions and state the multiplicity of each. Standard: 2.8.11.N. Solve linear, quadratic and exponential equations.

4. b.2x 3 + x 2 – 6x = 0 x (2x 2 + x – 6) = 0 x (2x – 3) (x + 2) = 0 x = 0, 3/2, and -2

5. c.5x 3 – 12x 2 + 4x = 0 x (5x 2 – 12x + 4) = 0 x (5x 2 – 12x + 4) = 0 x(5x – 2) (x – 2) = 0 x = 0, 2/5, and 2 x = 0, 2/5, and 2 Some polynomial equations have factors (and roots) that occur more than once.

7. b. x 3 + 2x 2 – 4x – 8 = 0 Use a graph, synthetic division, and factoring to find all of the roots of the following polynomial:

8. c. x 3 + 3x 2 – 4 = 0 Use a graph, synthetic division, and factoring to find all of the roots of the following polynomial:

9. If x – r is a factor that occurs m times in the factorization of a polynomial expression, P, then r is a root with multiplicity m of the related polynomial equation, P = 0. In example 2 above, 3 is a root with multiplicity 2 of the equation x 4 - 7x 2 + 15x – 9 = 0. When r is a root with even multiplicity, then the graph of the related function will touch but not cross the x-axis at (r, 0). Sometimes polynomials can be factored by using variable substitution.

12. x 4 – 9x 2 + 14 = 0 Use variable substitution and factoring to find all of the roots of the following polynomial:

13. x 4 – 5x 2 – 6 = 0 Use variable substitution and factoring to find all of the roots of the following polynomial:

14. Writing Activities

15. Review of Solving Polynomial Equations

17. Homework Integrated Algebra II- Section 7.4 Level A Honors Algebra II- Section 7.4 Level B