PPT-4.4 Real Zeros of Polynomial Functions

Understand the factor theorem Factor higher degree polynomials completely Analyze polynomials having multiple zeros Understand the rational zeros test and Descartes rule of signs Solve higher degree polynomial equations. Objectives: Identify Polynomial functions. Determine end behavior recognize characteristics of polynomial functions. Use factoring to find zeros of polynomial functions.. Polynomials of degree 2 or higher have graphs that are smooth and continuous. By smooth we mean the graphs have rounded curves with no sharp corners. By continuous we mean the graphs have no breaks and can be drawn without lifting your pencil from the rectangular coordinate system.. Unit . 3. Polynomial Functions. Section: . 5.1. Polynomial Functions . This section studies the . Polynomial Function. .. Your Goal - learn to . identify. the function components that lead to its . Chapter 6. Polynomial Functions. Polynomial Functions. A polynomial is a monomial or the sum of monomials.. A Polynomial Function:. P(x) = . a. n. x. n. + a. n-1. x. n-1 . + … + a. 1. x + a. 0. Where n is a nonnegative integer and the coefficients a. Polynomial Functions and their Graphs. October 15, 2015 Starter (3.2A). Describe the end behavior of the polynomial function to the left. October 15, 2015 Exit (3.2A). Explain the difference between an even function and an odd function when describing their end behavior.. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . 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. Taylor Johnson. (Taylor.Johnson@kctcs.edu). Elizabethtown Community . & . Technical College. Tools for Searching for Zeros . (1) Remainder Theorem. (2) Factor Theorem. (3) Intermediate Value Theorem. Now, we have learned about several properties for polynomial functions. Finding y-intercepts. Finding x-intercepts (zeros). End behavior (leading coefficient, degree). Testing values for zeros/factors (synthetic division) . Complex Numbers. Standard form of a complex number is: . a bi.. Every complex polynomial function of degree 1 or larger (no negative integers as exponents) has at least one complex zero.. a . and. b . 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. Objectives:. To approximate . x. -intercepts of a polynomial function with a graphing utility. To locate and use relative . extrema. of polynomial functions. To sketch the graphs of polynomial functions. What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN. functions. Linear. y = 4x - 5. Cubic. y = 4x. 3. - 5. Fifth Power. y = 4x. 5. –x 5. Quadratics. Objective: . Recognize the shape of basic polynomial functions. Describe the graph of a polynomial function. Identify properties of general polynomial functions: Continuity, End Behaviour, Intercepts, Local . 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..