Polynomials and Quadratic Equations for Algebra from Elevated Math

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 a² - b² (the difference of two squares), factoring polynomials in the form of x² + bx + c, and factoring polynomials of the form ax² + bx + c in which a ≠ 0 and a ≠ 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.

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