Report

P OLYNOMIALS P OLYNOMIAL D EFINITIONS Greatest (GCF) Common Factor Composite Number Prime Number Prime Polynomial Foil Method Factored Form Factoring Quadratic Expression Quadratic Equation Quadratic Formula Inverse Variation Product Rule Rational Function Rational Equation Extraneous Solutions P OLYNOMIALS What are polynomial and rational expressions and how can they be simplified? What are the characteristics of the graphs of rational functions? What are the techniques for solving rational equations? How can polynomial or rational expressions be connected to real world applications? P OLYNOMIAL AND R ATIONAL E XPRESSIONS R ATIONAL E QUATIONS & F UNCTIONS CLE 3102.3.2; SPI 3102.3.2; CFU 3102.3.7; CFU3102.3.2; SPI 8.1 Monomials and Factoring 3102.3.3; CFU3102.3.8; CLE 3102.3.8; SPI 3102.3.3; SPI 8.3 Quadratic Equations x2 + bx 3102.3.10; CFU +c=0 3102.3.3; CFU 3102.3.9 CLE 3102.3.8; SPI 8.4 Quadratic Equations ax2 + 3102.3.3; SPI bx + c = 0 3102.3.10 CLE 3102.3.8; SPI 8.5 Quadratic Equations 3102.3.10; SPI Difference of Squares 3102.3.3 7.6 Multiplying a Polynomial by a Mononmial 11.1 Inverse Variation 11.2 Rational Functions 11.3 Simplifying Rational Expressions 11.4 Multiplying and Dividing Rational Expressions 11.5 Dividing Polynomials 11.6 Adding and Subtracting Rational Expressions 11.8 Rational Equations Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials.; Operate with polynomials and simplify results.; Use various models (including area models) to represent products of polynomials. Find the GCF of the terms in a polynomial.; Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials.; Factor polynomials. Solve and understand solutions of quadratic equations with real roots.; Factor polynomials.; Find the solution of a quadratic equation and/or zeros of a quadratic function.; Justify correct results of algebraic procedures using extension of properties of real numbers to algebraic expressions.; Find two binomial factors of a quadratic expression. Solve and understand solutions of quadratic equations with real roots.; Factor polynomials.; Find the solution of a quadratic equation and/or zeros of a quadratic function. Solve and understand solutions of quadratic equations with real roots.; Find the solution of a quadratic equation and/or zeros of a quadratic function.; Factor polynomials. Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, CFU3102.3.19; quadratic, and square root function. Use technology where appropriate.; Use technologies appropriately to CLE 3102.1.7; SPI develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate 3102.1.2 and reliable models.; Write an equation symbolically to express a contextual problem. Understand and use relations and functions in various representations to solve contextual problems.; Operate CLE 3102.3.6; SPI with, evaluate, and simplify rational expressions including determining restrictions on the domain of the 3102.3.4; SPI variables.; Determine domain and range of a relation, determine whether a relation is a function and/or 3102.3.7 evaluate a function at a specified rational value. CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Operate with, evaluate, and 3102.3.4; SPI simplify rational expressions including determining restrictions on the domain of the variables.; Apply 3102.1.3 properties to evaluate expressions, simplify expressions, and justify solutions to problems. CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Operate with, evaluate, and 3102.3.4; simplify rational expressions including determining restrictions on the domain of the variables. CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Find the solution of a quadratic 3102.3.10 equation and/or zeros of a quadratic function. CFU3102.3.10; Add, subtract, multiply, and divide rational expressions and simplify results.; Understand and apply CLE 3102.3.3; SPI operations with rational expressions and equations.; Operate with, evaluate, and simplify rational 3102.3.4 expressions including determining restrictions on the domain of the variables. CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Determine domain and range of a 3102.3.7 relation, determine whether a relation is a function and/or evaluate a function at a specified rational value. 7.6 M ULTIPLY A P OLYNOMIAL BY A M ONOMIAL CLE 3102.3.2 Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials. SPI 3102.3.2 Operate with polynomials and simplify results. CFU 3102.3.7 Use various models (including area models) to represent products of polynomials. D ISTRIBUTIVE P ROPERTY M ODELING WITH A LGEBRA T ILES 2 X ( X + 3) X =2 X 2 + 6 X 1 1 1 X X2 X X X X X2 X X X M ODELING WITH A LGEBRA T ILES 3 X ( X - 2) X =3 X 2 – 6 X 1 1 X X2 X X X X2 X X X X2 X X M ODELING WITH A LGEBRA T ILES 2 X ( X - 4) X =2 X 2 – 8 X 1 1 1 1 X X2 X X X X X X2 X X X X M ULTIPLY M ONOMIAL VS P OLYNOMIAL Use Distributive Property -2x2(3x2 -7x + 10) -2x2(3x2) = -6x4 -2x2(-7x) = +14x3 -2x2(+ 10) = -20x2 = -6x4 +14x3 -20x2 S IMPLIFY THE Use Distributive Property 3(2t2-4t-15) + 6t(5t + 2) Combine Like Terms 6t2-12t-45 + 30t2 + 12t 36t2 +0t -45 36t2 - 45 E QUATION P RACTICE A SSIGNMENT Page 442, 18 – 30 even DO ALL EVEN LATE ASSIGNMENTS WILL NEED TO DO PAGE 831 1-6 ADDITIONAL