The 23 lessons in this group provide initial instruction or intervention on polynomials and quadratic equations. In the first seven lessons students ...
The 23 lessons in this group provide initial instruction or intervention on polynomials and quadratic equations. In the first seven lessons students learn the rules of exponents, scientific notation of simplified algebraic expressions, how to add and subtract polynomials, how to multiply polynomials, how to multiply monomials and polynomials, how to divide polynomials by monomials, and how to divide polynomials using long division. Mastery of these skills is necessary to understand factoring, and a thorough understanding of factoring is necessary to solve quadratic equations. A11.1 Applying Rules of Exponents A11.2 Using Scientific Notation A11.3 Adding and Subtracting Polynomials A11.4 Multiplying Monomials and Binomials A11.5 Multiplying Polynomials A11.6 Dividing Polynomials A11.7 Dividing Polynomials Using Long Division The next seven lessons show the student step-by-step how to factor polynomials. Polynomials are algebraic expressions that use only three basic operations (addition, subtraction, multiplication) on whole number exponents. Students learn several methods of factoring polynomials, among them are: factoring to remove the greatest common factor, factoring by groups, factoring polynomials in the form of aÂ² - bÂ² (the difference of two squares), factoring polynomials in the form of xÂ² + bx + c, and factoring polynomials of the form axÂ² + bx + c in which a â‰ 0 and a â‰ 1. Factoring is used throughout mathematics. It is used in geometry to solve problems involving area, in trigonometry to solve equations, and in calculus to find the limits of a function. A12.1 Factoring by Removing the Greatest Common Factor A12.2 Factoring by Grouping A12.3 Factoring the Difference of Two Squares A12.4 Factoring + + A12.5 Factoring + + A12.6 Factoring Using Several Methods A12.7 Dividing Polynomials Using Factoring In the next six lessons students distinguish between quadratic and linear equations and learn several methods for solving quadratic equations. Manufacturers use quadratic equations to maximize revenue by adjusting price according to demand. Business owners use quadratic equations to manipulate variables such as cost and profit. A13.1 Defining Quadratic Equations of One Variable A13.2 Solving Quadratic Equations by Evaluating Square Roots A13.3 Solving Quadratic Equations by Factoring A13.4 Solving Quadratic Equations by Completing the Square A13.5 Solving Quadratic Equations by the Quadratic Formula A13.6 Solving Problems Using Quadratic Equations of One Variable The last three lessons in this group focus on graphing quadratic relations. Students learn to identify the shape, orientation, and location in the coordinate plane of a parabola by analyzing its equation. They solve application problems using the graphs of quadratic relations to find maximum and minimum values. A14.1 Graphing Simple Quadratic Relations A14.2 Graphing Quadratic Relations by Analysis 14.3 Solving Problems Using Quadratic Graphs Student print materials and Teachers' Notes are available for download at www.elevatedmath.com. Download the free Elevated Math app to view two complimentary lessons or buy the lessons individually.
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