Review of Factoring; Quadratic Equations and Rational

Slides:

Advertisements

Similar presentations

Section 5.1 Quadratic Equations.

Advertisements

Ch. 5 Polynomials, Polynomial Functions, & Factoring

Elementary Algebra A review of concepts and computational skills Chapters 5-7.

MAT 105 SPRING 2009 Factoring and Algebraic Fractions

6 – 4: Factoring and Solving Polynomial Equations (Day 1)

Other Types of Equations

Section 5.4 Factoring FACTORING Greatest Common Factor,

EXPONENTS AND POLYNOMIALS College Algebra. Integral Exponents and Scientific Notation Positive and negative exponents Product rule for exponents Zero.

Several Methods 1.Trial and Error – More mental math 2.Grouping – Longer method FACTORING TRINOMIALS WITH LEADING COEFFICIENT > 1.

Section 5.1 Polynomials Addition And Subtraction.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 6 Factoring.

Algebra Core Review Day 7

Trigonometry/ Pre-Calculus Chapter P: Prerequisites Section P.4: Solving Equations Algebraically.

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 5.6 Factoring a Polynomial We have looked at factoring out a.

Factoring Special Products

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

Factoring and Solving Polynomial Equations Chapter 6.4.

Section 6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials.

Copyright © Cengage Learning. All rights reserved. Factoring Polynomials and Solving Equations by Factoring 5.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 6 Factoring.

Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression

Factoring and Solving Polynomial Equations (Day 1)

Special Cases of Factoring Chapter 5.5 Perfect Square Trinomials a 2 + 2ab + b 2 (a + b) 2 = a 2 – 2ab + b 2 (a – b) 2 =

Solving Quadratics: Factoring. What is a factor? Numbers you can multiply to get another number 2  3.

Lesson 10.5 Factoring Objective: To factor a quadratic trinomial of the form Factoring a trinomial is the opposite of multiplying two binomials. Example:

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 5.6 A Strategy for Factoring Polynomials, page If there.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 1.

§ 5.6 A General Factoring Strategy. Blitzer, Intermediate Algebra, 4e – Slide #81 A Strategy for Factoring Polynomials A Strategy for Factoring a Polynomial.

5 – 2: Solving Quadratic Equations by Factoring Objective: CA 8: Students solve and graph quadratic equations by factoring, completing the square, or using.

REVIEW OF FACTORING Chapters 5.1 – 5.6. Factors Factors are numbers or variables that are multiplied in a multiplication problem. Factor an expression.

Section 10.6 Factoring Objectives: Factor a quadratic expression of the form Solve quadratic equations by factoring.

Factoring Polynomials Section 2.4 Standards Addressed: A , A , CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.5.

Chapter 6 Section 6 Solving Rational Equations. A rational equation is one that contains one or more rational (fractional) expressions. Solving Rational.

Chapter 5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Factoring.

Mark Dugopolski Elementary Algebra Edition 3 Chapter 5 Factoring Copyright © 2000 by the McGraw-Hill Companies, Inc.

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 6.5, Slide 1 Chapter 6 Polynomial Functions.

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental.

Essential Question: What must you do to find the solutions of a rational equation?

9-2 Factoring Using the Distributive Property Objectives: 1)Students will be able to factor polynomials using the distributive property 2)Solve quadratic.

Factor and Solve Polynomial Equations Homework Questions?

10.6 Solving Rational Equations Rational Equation An equation containing one or more rational expressions.

Notes Over 10.7 Factoring Special Products Difference of Two Squares.

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 6.6, Slide 1 Chapter 6 Polynomial Functions.

Copyright © 2013, 2009, 2006 Pearson Education, Inc.

Notes Over 10.8 Methods of Factoring Binomial Trinomial

Bellwork Multiply (x+2)(x+3) 2) Put in Vertex Form 3)

Polynomials and Polynomial Functions

Module 3.3 Factoring.

Section 6.4: Factoring Polynomials

Objectives Factor out the greatest common factor of a polynomial.

CHAPTER R: Basic Concepts of Algebra

Factoring Polynomials

Factoring Polynomials

4.5 & 4.6 Factoring Polynomials & Solving by Factoring

Warm Up Factor each expression. 1. 3x – 6y 3(x – 2y) 2. a2 – b2

Section R.4 Factoring.

8.6 Solving Rational Equations

Copyright © Cengage Learning. All rights reserved.

Chapter 6 Section 4.

What You Will Learn Solving Quadratic Equations by Using Factoring

Polynomials and Polynomial Functions

5.4 Factor and Solve Polynomial Equations

Factor & Solve Polynomial Equations

Factoring and Completing the Square Review

4.2: Solving Rational Equations

The Greatest Common Factor

Chapter 6 Section 4.

3.4 Solve by Factoring (Part 1)

11-5 Solving Rational Equations

Presentation transcript:

Review of Factoring; Quadratic Equations and Rational Chapter 8 A Transition Section 4 Review of Factoring; Quadratic Equations and Rational Equations

Test-Taking Strategies Preparation

Factoring Polynomials (page 1) Factor out any common factors. Determine the number of terms in the polynomial. If there are only 2 terms, check to see if the binomial is one of the special binomials. Difference of Squares: Sum of Squares: is not factorable Difference of Cubes: Sum of Cubes:

Factoring Polynomials (page 2) If there are 3 terms, try to use one of the following techniques. Find two integers m and n whose product is c and whose sum is b. Factor by grouping or by trial and error. If there are 4 terms, try factoring by grouping. After the polynomial has been factored, be sure that any factor with two or more terms does not have any common factors other than 1. If there are common factors, factor them out. Check your factoring through multiplication.

Factoring Polynomials 1 Factoring Polynomials Factor: GCF:

Factoring Polynomials 2 Factoring Polynomials Factor: Difference of Squares

Factoring Polynomials 3 Factoring Polynomials Factor: Difference of Cubes

Factoring Polynomials 4 Factoring Polynomials Factor: Sum of Cubes

Factoring Polynomials 5 Factoring Polynomials Factor: Trinomial, Leading Coefficient of 1

Factoring Polynomials 6 Factoring Polynomials Factor: Trinomial, Leading Coefficient of 1

Factoring Polynomials 7 Factoring Polynomials Factor: Trinomial, Leading Coefficient Other Than 1

Factoring Polynomials 8 Factoring Polynomials Factor: Factor by grouping

Solving Quadratic Equations by Factoring Write the equation in standard form: Factor the expression completely. Set each factor equal to 0 and solve the resulting equations. Check your solutions.

Solving Quadratic Equations by Factoring 9 Solving Quadratic Equations by Factoring Solve:

Solving Rational Equations Find the LCD of all rational expressions in the equation and then multiply both sides of the equation by that LCD. Solve the resulting equation. Check for extraneous solutions.

Solving Rational Equations (page 1) 10 Solve: LCD:

Solving Rational Equations (page 2) 11 Extraneous Solution