7.4 Solving Polynomial Equations

1. 7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each. Standard: 2.8.11.N. Solve linear, quadratic and exponential equations.

3. 2x3+ x2– 6x = 0 x (2x2 + x – 6) x (2x – 3) (x + 2) x = 0, 3/2, and -2

4. 5x3– 12x2 + 4x = 0 x (5x2 – 12x + 4) x(5x – 2) (x – 2) x = 0, 2/5, and 2 Some polynomial equations have factors (and roots) that occur more than once.

6. b.x3+ 2x2 – 4x – 8 = 0 Use a graph, synthetic division, and factoring to find all of the roots of the following polynomial:

7. c. x3 + 3x2 – 4 = 0 Use a graph, synthetic division, and factoring to find all of the roots of the following polynomial:

8. 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 x4 - 7x2 + 15x – 9 = 0. When r is a root with even multiplicity, then the graph of the related function will touchbut not cross the x-axis at (r, 0). Sometimes polynomials can be factored by using variable substitution.

11. Use variable substitution and factoring to find all of the roots of the following polynomial: x4 – 9x2 + 14 = 0

12. Use variable substitution and factoring to find all of the roots of the following polynomial: x4 – 5x2 – 6 = 0

13. Writing Activities

14. Review ofSolving Polynomial Equations

15. Homework Pg. 453 #12-50 even