6.3 Synthetic Division.

Slides:

Advertisements

Similar presentations

COMBINED PROBLEMS The Remainder / Factor Theorems along with Synthetic Division help factor higher order polynomials quickly.

Advertisements

7.4 Remainder and Factor Theorems 7.5 Roots and Zeros

Warm up Use synthetic division to divide (4x3 – 3x2 + 2x + 1)/ (x – 1) (x3 – x2 – 6)/(x + 2)

Long Division of Polynomials

Unit 3 Practice Test Review. 1a) List all possible rational zeros of this polynomial: 5x 4 – 31x x 2 – 31x + 6 p  1, 2, 3, 6 q  1, 5 p  1, 2,

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

Pre Calc Lesson 2.2 Synthetic Division ‘Remainder’ and ‘Factor’ Theorems Review Long Division: 5365 ÷ 27 Now review ‘long division’ of polynomials: (2x.

Dividing Polynomials; Remainder and Factor Theorems.

The Remainder and Factor Theorems Check for Understanding 2.3 – Factor polynomials using a variety of methods including the factor theorem, synthetic division,

5.5 Apply the Remainder and Factor Theorem

Remainder and Factor Theorem Unit 11. Definitions Roots and Zeros: The real number, r, is a zero of f(x) iff: 1.) r is a solution, or root of f(x)=0 2.)

Warm Up #1 1. Use synthetic substitution to evaluate f (x) = x3 + x2 – 3x – 10 when x = – ANSWER –4.

Find Rational Zeros, I Objectives: 1.To find the zeros of a polynomial function 2.To use the Rational Zero Theorem to find the possible rational zeros.

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

Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.

Division and Factors When we divide one polynomial by another, we obtain a quotient and a remainder. If the remainder is 0, then the divisor is a factor.

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

TH EDITION LIAL HORNSBY SCHNEIDER COLLEGE ALGEBRA.

Real Zeros of Polynomial Functions. Quick Review.

1 What we will learn today…  How to divide polynomials and relate the result to the remainder and factor theorems  How to use polynomial division.

5.3 Part 2 Polynomial Division

The Remainder and Factor Theorems

Complex Numbers, Division of Polynomials & Roots.

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

1 Use the Remainder Theorem and the Factor Theorem. 2.3 Day 2 What You Should Learn.

Synthetic Evaluation of Polynomials Be able to use synthetic division to evaluate polynomials.

Section 5.3(d) Synthetic Substitution. Long division Synthetic Division can be used to find the value of a function. This process is called Synthetic.

2.4/2.52.4/2.5 Real Zeros of Polynomial Functions.

Section 2-2 Synthetic Division; The Remainder and Factor Theorems.

7.3 Products and Factors of Polynomials Objectives: Multiply polynomials, and divide one polynomial by another by using long division and synthetic division.

Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.

3.6 Day 2 Why Synthetic Division? What use is this method, besides the obvious saving of time and paper?

Using theorems to factor polynomials.  If a polynomial f(x) is divided by x-k, then the remainder r = f(k)  This is saying, when you divide (using synthetic.

7.4 Solving Polynomial Equations

Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.

Algebra II Explorations Review ( ) Day Divide using LONG Division. Show all work. Answer:

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.

Polynomial and Synthetic Division Objective: To solve polynomial equations by long division and synthetic division.

Section 4.3 Polynomial Division; The Remainder and Factor Theorems Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Dividing Polynomials Section 4.3.

Divide x3 + x2 – 10x + 8 by x+4 using long division.

Warm Up Compute the following by using long division.

3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6x

Section 5.4 – Dividing Polynomials

Essential Questions How do we use long division and synthetic division to divide polynomials?

LIAL HORNSBY SCHNEIDER

Synthetic Division and Linear Factors

Unit 9: Polynomial Operations

Dividing Polynomials: Synthetic Division

7.4 The Remainder and Factor Theorems

The Remainder and Factor Theorems

Dividing Polynomials Long Division A little review:

Dividing Polynomials.

1a. Divide using long division. (9x3 – 48x2 + 13x + 3) ÷ (x – 5)

4.1 Notes day 2 Remainder Theorem: If a polynomial f(x) is divided by x – c, then the remainder is f(c). Ex. f(x) = x3 + 3 divided by g(x)= x -1.

DIVIDING POLYNOMIALS Synthetically!

Packet #8 Dividing Polynomials

Apply the Remainder and Factor Theorems

6.5 The Remainder and Factor Theorems

Essential Question: How do I divide polynomials?

Section 3 – The Remainder and Factor Theorems

Remainder and Factor Theorem

Dividing Polynomials WOW! I want to learn how to do that?

The Remainder and Factor Theorems

4.3 – The Remainder and Factor Theorems

What is synthetic division?

The Remainder and Factor Theorems

Copyright © Cengage Learning. All rights reserved.

Presentation transcript:

6.3 Synthetic Division

Here is a quick way to evaluate the value of a function for a particular value of x. It is called synthetic substitution. Evaluate for x = 3 129 15 39 5 13 43 124 The value of the function is 124 when x = 3

Use synthetic substitution to find the value of y when x = 2 The value of the function is -100 when x = 2

Use synthetic substitution to find the value of y when x = -2 The value of the function is 0 when x = -2 This means that x = -2 is a root of the function.

Since x = -2 is a root of the function, we know that…. Divide x4 + 5x3 –3x2 +45x –54 by x + 2 to determine what the something in the parentheses is:

Divide

Compare 1 3 -9 -27 0 Now compare this result to what you got when you did synthetic substitution. What do you notice? Synthetic Substitution is the same as Long Division!!!! (Except that it only works for linear factors)

Conclusion: Since synthetic substitution, synthetic division, and long division are essentially the same process…. We can use synthetic division in most cases instead of long division.

Divide:

Divide: Since the remainder is zero (x+3) is a factor.

Divide: Since the remainder is zero (x - 9) is a factor.

What would happen if your divided repeatedly? This polynomial has roots at x = 1 and –2 (and no others)

What would happen if your divided repeatedly? This polynomial has roots at x = 1 and –2 (and no others) Extra Space for division

Factor completely using synthetic division. This polynomial has roots at x = 2 and 3 (and no others)

Factor completely using synthetic division. This polynomial has roots at x = 2 and 3 (and no others) Extra Space for division