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

Slides:

Advertisements

Similar presentations

Remainder and Factor Theorems

Advertisements

Long and Synthetic Division of Polynomials Section 2-3.

Dividing Polynomials Objectives

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

5.3 Division of Polynomials. Dividing a Polynomial by a monomial.  Divide each term of the polynomial by the monomial.

Synthetic Division Dela Peña, Kenneth A.. - is a shorthand, or shortcut, method of dividing polynomial by a binomial of the form x – b. Synthetic Division.

EXAMPLE 1 Use polynomial long division

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

Synthetic Division. This method is used to divide polynomials, one of which is a binomial of degree one.

Dividing Polynomials  Depends on the situation.  Situation I: Polynomial Monomial  Solution is to divide each term in the numerator by the monomial.

HW: Pg #13-61 eoo.

Section 7.3 Products and Factors of Polynomials.

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.

Polynomial Division and the Remainder Theorem Section 9.4.

3.2 Dividing Polynomials 11/28/2012. Review: Quotient of Powers Ex. In general:

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.

Multiply polynomials vertically and horizontally

Algebraic long division Divide 2x³ + 3x² - x + 1 by x + 2 x + 2 is the divisor The quotient will be here. 2x³ + 3x² - x + 1 is the dividend.

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.

7.4 The Remainder and Factor Theorems Use Synthetic Substitution to find Remainders.

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.

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?

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

Section 5.5. Dividing a Polynomial by a Polynomial The objective is to be able to divide a polynomial by a polynomial by using long division. Dividend.

Quotient Dividend Remainder Divisor Long Division.

Table of Contents Polynomials: Synthetic Division If a polynomial is divided by a linear factor of the form x – c, then a process know as 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.

Products and Factors of Polynomials (part 2 of 2) Section 440 beginning on page 442.

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

Objective Use long division and synthetic division to divide polynomials.

Warm Up Divide using long division ÷ ÷

Dividing Polynomials Section 4.3.

Name:__________ warm-up 5-2 Quiz – 5-1

Polynomial Division.

#2.5 Long Division.

Synthetic Division.

Dividing Polynomials: Synthetic Division

Dividing Polynomials.

7.4 The Remainder and Factor Theorems

Binomial Theorem Honor’s Algebra II.

Dividing Polynomials.

Objective Use long division and synthetic division to divide polynomials.

Dividing Polynomials.

Dividing Polynomials.

Polynomial and Synthetic Division

Dividing Polynomials.

Dividing Polynomials.

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.

Dividing Polynomials.

Dividing Polynomials.

4.3 Synthetic Division Objectives:

Synthetic Division.

Synthetic Division The shortcut.

Divide using long division

Synthetic Division Notes

Presentation transcript:

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

Example 1

Remainder Theorem

Synthetic Division: A process for division of a polynomial by a binomial. Example 2: Divide

Step 1: Write the terms of the polynomial in descending order. Then write just the coefficients as shown.

Step 2: Write the constant k, of the divisor x – k to the left Bring the first coefficient down. Multiply the first coefficient by k and write the product under the second coefficient. Add the second column. Write the sum as shown.

To write the result

Example 3:

Factor Theorem

Example 4 x = 2 Subtract 2 from both sides x – 2 = 0 So, x – 2 is a factor

The result gives the coefficients of the quotient.

HOMEWORK: AM Objectives #81 Divide Polynomials #82 Long division, factor higher term polynomials

Example 4 Factor

Use synthetic division to find the other factors. The result gives the coefficients quotient