Example 3 Break-Even Chapter 6.4 The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To.

Slides:

Advertisements

Similar presentations

Dividing Polynomials.

Advertisements

Remainder and Factor Theorems

Long and Synthetic Division of Polynomials Section 2-3.

Chapter 2 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Dividing Polynomials: Remainder and Factor Theorems.

Warm-Up: January 5, 2012  Use long division (no calculators) to divide.

Dividing Polynomials Objectives

Polynomials Functions Review (2)

5-4 Dividing Polynomials Long Division Today’s Objective: I can divide polynomials.

Example 1 divisor dividend quotient remainder Remainder Theorem: The remainder is the value of the function evaluated for a given value.

Long Division of Polynomials

Copyright © Cengage Learning. All rights reserved. Polynomial And Rational Functions.

Warm up. Lesson 4-3 The Remainder and Factor Theorems Objective: To use the remainder theorem in dividing polynomials.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 3 Polynomial and Rational Functions.

Example 2 Combining Graphical and Algebraic Methods Chapter 6.4 Solve the equation.

Section 7.3 Products and Factors of Polynomials.

Dividing Polynomials 3

6.8 Synthetic Division. Polynomial Division, Factors, and Remainders In this section, we will look at two methods to divide polynomials: long division.

Lesson 2.4, page 301 Dividing Polynomials Objective: To divide polynomials using long and synthetic division, and to use the remainder and factor theorems.

Polynomial Division, Factors, and Remainders ©2001 by R. Villar All Rights Reserved.

Copyright © 2009 Pearson Education, Inc. CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions.

5-3 Dividing Polynomials Objectives Students will be able to: 1) Divide polynomials using long division 2) Divide polynomials using synthetic division.

Warm up  Divide using polynomial long division:  n 2 – 9n – 22 n+2.

UNIT 2 – QUADRATIC, POLYNOMIAL, AND RADICAL EQUATIONS AND INEQUALITIES Chapter 6 – Polynomial Functions 6.3 – Dividing Polynomials.

5. Divide 4723 by 5. Long Division: Steps in Dividing Whole Numbers Example: 4716  5 STEPS 1. The dividend is The divisor is 5. Write.

6.3 Dividing Polynomials 1. When dividing by a monomial: Divide each term by the denominator separately 2.

Objective Use long division and synthetic division to divide polynomials.

4-3 The Remainder and Factor Theorems

5.5: Apply Remainder and Factor Theorems (Dividing Polynomials) Learning Target: Learn to complete polynomial division using polynomial long division and.

Chapter 1 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Dividing Polynomials; Remainder and Factor Theorems.

6-5: The Remainder and Factor Theorems Objective: Divide polynomials and relate the results to the remainder theorem.

Dividing Polynomials Day #2 Advanced Math Topics Mrs. Mongold.

Synthetic Division. Review: What is a polynomial? How do we know the degree of the polynomial?

a. b.  To simplify this process, we can use a process called division.  Synthetic division works when dividing a polynomial by.  To get started, make.

Quotient Dividend Remainder Divisor Long Division.

Division of Polynomials Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Dividing Polynomials Long division of polynomials.

WARM UP Simplify DIVISION OF POLYNOMIALS OBJECTIVES  Divide a polynomial by a monomial.  Divide two polynomials when the divisor is not a monomial.

5-4 Dividing Polynomials Synthetic Division

Let’s look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every.

Holt Algebra Dividing Polynomials Synthetic division is a shorthand method of dividing a polynomial by a linear binomial by using only the coefficients.

Key Vocabulary: Dividend Divisor Quotient Remainder.

College Algebra Chapter 3 Polynomial and Rational Functions Section 3.3 Division of Polynomials and the Remainder and Factor Theorems.

Chapter 5 Section 5. EXAMPLE 1 Use polynomial long division Divide f (x) = 3x 4 – 5x 3 + 4x – 6 by x 2 – 3x + 5. SOLUTION Write polynomial division.

Unit 3.3- Polynomial Equations Continued. Objectives  Divide polynomials with synthetic division  Combine graphical and algebraic methods to solve polynomial.

Dividing Polynomials: Synthetic Division. Essential Question  How do I use synthetic division to determine if something is a factor of a polynomial?

3.2 Division of Polynomials. Remember this? Synthetic Division 1. The divisor must be a binomial. 2. The divisor must be linear (degree = 1) 3. The.

Objective Use long division and synthetic division to divide polynomials.

Warm Up Divide using long division ÷ ÷

Reminder steps for Long Division

Warm-up 6-5 1) 2).

Lesson 6-5: Synthetic Division

Synthetic Division.

Dividing Polynomials.

Section 2.4 Dividing Polynomials; Remainder and Factor Theorems

Apply the Remainder and Factor Theorems Lesson 2.5

4.3 Division of Polynomials

Objective Use long division and synthetic division to divide polynomials.

Division of Polynomials and the Remainder and Factor Theorems

Dividing Polynomials.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Warm Up 1. Simplify, then write in standard form (x4 – 5x5 + 3x3) – (-5x5 + 3x3) 2. Multiply then write in standard form (x + 4) (x3 – 2x – 10)

Synthetic Division.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Dividing Polynomials.

Synthetic Division.

Synthetic Division The shortcut.

Keeper 11 Honors Algebra II

Divide using long division

Presentation transcript:

example 3 Break-Even Chapter 6.4 The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, a.Graph the function using a window representing up to 50 thousand units and find one x-intercept of the graph. b.Use synthetic division to find a quadratic factor of P(x). c.Find all of the zeros of P(x). d.Determine the levels of production that give break-even.  2009 PBLPathways

The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, a.Graph the function using a window representing up to 50 thousand units and find one x-intercept of the graph. b.Use synthetic division to find a quadratic factor of P(x). c.Find all of the zeros of P(x). d.Determine the levels of production that give break-even.

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, a.Graph the function using a window representing up to 50 thousand units and find one x-intercept of the graph. x P(x) (20, 0)

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, a.Graph the function using a window representing up to 50 thousand units and find one x-intercept of the graph. x P(x) (20, 0)

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, a.Graph the function using a window representing up to 50 thousand units and find one x-intercept of the graph. x P(x)

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, a.Graph the function using a window representing up to 50 thousand units and find one x-intercept of the graph. x P(x) (20, 0)

 2009 PBLPathways 1.Arrange the coefficients in descending powers of x, with a 0 for any missing power. Place a from x - a to the left of the coefficients. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways 1.Arrange the coefficients in descending powers of x, with a 0 for any missing power. Place a from x - a to the left of the coefficients. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways 2.Bring down the first coefficient to the third line. Multiply the last number in the third line by a and write the product in the second line under the next term. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways 2.Bring down the first coefficient to the third line. Multiply the last number in the third line by a and write the product in the second line under the next term. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x). Multiply

 2009 PBLPathways 3.Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways 3.Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways 3.Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways 3.Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used. The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x). 3.Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used.

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x). 4.The third line represents the coefficients of the quotient, with the last number the remainder. The quotient is a polynomial of degree one less than the dividend. Remainder Coefficients of quotient

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, b.Use synthetic division to find a quadratic factor of P(x). 4.If the remainder is 0, x – a is a factor of the polynomial, and the polynomial can be written as the product of the divisor x - a and the quotient. Remainder Coefficients of quotient

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, c.Find all of the zeros of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, c.Find all of the zeros of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, c.Find all of the zeros of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, c.Find all of the zeros of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, c.Find all of the zeros of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, c.Find all of the zeros of P(x).

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, d.Determine the levels of production that give break-even. x P(x) (-10,0) (20,0) (100,0)

 2009 PBLPathways The weekly profit for a product is thousand dollars, where x is the number of thousands of units produced and sold. To find the number of units that gives break-even, d.Determine the levels of production that give break-even. x P(x) (-10,0) (20,0) (100,0) Break-even points