PPT-Finding Zeros of Polynomial Functions

Taylor Johnson TaylorJohnsonkctcsedu Elizabethtown Community amp Technical College Tools for Searching for Zeros 1 Remainder Theorem 2 Factor Theorem 3 Intermediate Value Theorem. Common Core II – Day 2. Warm Ups. a) Factor to solve the equation x. 2. – 7x + 10 = 0. . b) Explain what the solutions tell you about the graph. . c. ) Using what you know about the quadratic function, draw a rough sketch.. 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 . 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.. Chapter 5.6. Review: Zeros of Quadratic Functions. In the previous chapter, you learned several methods for solving quadratic equations. If, rather than a quadratic equation . , we think about the function .  . 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. Polynomial Function. Definition: A polynomial function of degree . n. in the variable x is a function defined by. Where each . a. i. (0 ≤ . i. ≤ n-1) is a real number, a. n. ≠ 0, and n is a whole number. . Defn. : . Polynomial function. In the form of: . ..  . The coefficients are real numbers.. The exponents are non-negative integers.. The domain of the function is the set of all real numbers.. What is a . rational . function?. Definition: . A function of the form . , where . and . are polynomials and . is not the zero polynomial.. What . is the most common form of the equation?.  . What does it look like?. 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].. 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) . Section 2.4. Terms. Divisor: . Quotient: . Remainder:. Dividend: . PF. FF .  . Long Division. Use long division to find . divided by . ..  . Division Algorithm for Polynomials. Let . and . be polynomials with the degree of . 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.