PPT-Solving Polynomial Equations

Section 45 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. 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 TYPE EXAMPLE General trinomial 2 57530 5 57530 12 2 3 57530 Perfect square trinomial 10 25 5 Difference of two squares 57530 2 3 2 57530 3 Common monomial factor 15 3 2 5 In this lesson you will learn how to factor other types of poly Lesson Objective:. An equation is like a set of scales.. To keep it balanced, whatever you. do to one side you must do to the other.. Use this idea to solve equations like:. 3x + 1 = x + 7 . 2 (3x + 1) = 3 (x – 2). Multiplication . Equations. 3-3 Solving . Multiplication . Equations. Solve. Solution. GOAL. Find the value of the variable that makes the. equation TRUE.. The value that makes the equation true.. To isolate the variable (have the variable on one. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Problem 1. There are 25 toys in a playground. . The toys are either bicycles (2 wheels) or tricycles (3 wheels). . In total in the playground there are 61 wheels. . How many bicycles are in the playground?. Mathematical Language. A . solution. of an equation is a number that make the equation true. 3x+2=17. To . solve. an equation means to find all its solution. Two equations are equivalent if they have the same solutions. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Equations Using Algebra Tiles . Objectives. Solving Equations Involving the Distributive Property. Solving Multi-Step Equations. Solving Equations. The development of the equation solving model is based on two ideas.. 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”. 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. GCSE: Solving Quadratic Equations Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 2 nd June 2015 Overview There are 4 ways in which we can solve quadratic equations.   1 By Factorising 2 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..