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. Mrs. . Chernowski. Pre-Calculus. Chris Murphy. Requirements:. At least 3 relative maxima and/or minima. The ride length must be at least 4 minutes. The coaster ride starts at 250 feet. The ride dives below the ground into a tunnel at least once. 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.. Zuzana. . Kukelova. , Martin . Bujnak. , Tomas . Pajdla. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. A. A. Motivation. Recognition & Tracking. Classify polynomials and write polynomials in standard form. . Evaluate . polynomial expressions. .. Add and subtract polynomials. . Objectives. monomial. degree of a monomial. polynomial. degree of a polynomial.  . 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. . 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. 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 . 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. 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 .