PPT-Unit 3.3- Polynomial Equations

Continued Objectives Divide polynomials with synthetic division Combine graphical and algebraic methods to solve polynomial equations Use the Fundamental Theorem of Algebra to find the number of complex solutions of a polynomial equation. A polynomial in of degree where is an integer is an expression of the form 1 where 0 a a are constants When is set equal to zero the resulting equation 0 2 is called a polynomial equation of degree In this unit we are concerned with the number Simplify:. . . (0.04 x 10 )(50 x 10 ). . (0.000004)(50,000). -9 16. Answer:. 1 x 10 . 8. Lesson 81:. Graphical Solutions, Inconsistent Equations, Dependent Equations.  . An order . differential equation has a . parameter family of solutions … or will it?.  . 0. 1. 2. 3. 4. 0. 0. 1. 2. 3. 4. 1. 1. 2. 3. 4. 0. 2. 2. 3. 4. 0. 1. 3. 3. 4. 0. 1. 2. 4. 4. 0. 1. 2. Algebra 2. Chapter 5. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Quadratic Function. A . quadratic function . is defined by a quadratic or second-degree polynomial.. Standard Form. , . where . a. . ≠ 0. .. Vertex Form. , where a. . ≠ 0..  . Vertex and Axis of Symmetry. . A Reminiscence 1980-1988. Alexander Morgan. Part of the Prehistory of Applied Algebraic Geometry. A Series of (Fortunate) Unlikely Events. Intellectual epidemiology: . Idea originates with “case zero”. Section 4.5 beginning on page 190. Solving By Factoring. We already know how the zero product property allows us to solve quadratic equations, this property also allows us to solve factored polynomial equations [we learned how to factor polynomial expressions in the previous section].. , 2009. Subdivision methods for solving polynomial . equations. 1. abstract. The purpose of the talk today is to present . a new algorithm. . for . solving . a system of . polynomials. in a domain . Section 4.1. Polynomial Functions. Determine roots of polynomial equations. Apply the Fundamental Theorem of Algebra. Polynomial in one variable. A polynomial in one variable x, is an expression of the form a. Review of Factoring. 2. nd. Degree Polynomials. x. 2. 9x 20 . = (x 5)(x 4). . x. 2. - 11x 30. = (x-6)(x-5). . 3x. 2. 20x 12. . = (3x 2)(x 6) . Factoring of higher-degree polynomials. Standard 15. Graph and analyze polynomial and radical functions to determine:. Domain and range. X and y intercepts. Maximum and minimum values. Intervals of increasing and decreasing. End behavior. With the function: f(x) = . Anchor rates based on literature review. The “anchor rates” were the rates of percent Total Phosphorus removal based on the runoff treated in inches as was derived from the expert panel literature review. . NC Math 31North Carolina Standard Course of StudyNorth Carolina Math 3Standards for Mathematical Practice1Make sense of problems and persevere in solving them2Reason abstractly and 3Construct viable a Algebra 2. Chapter 4. This Slideshow was developed to accompany the textbook. Big Ideas Algebra 2. By Larson, R., Boswell. 2022 K12 (National Geographic/Cengage). Some examples and diagrams are taken from the textbook..