Polynomial Long Division

Slides:

Advertisements

Similar presentations

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

Advertisements

Dividing Polynomials Section 2.4. Objectives Divide two polynomials using either long division or synthetic division. Use the Factor Theorem to show that.

4.4 Notes The Rational Root Theorem. 4.4 Notes To solve a polynomial equation, begin by getting the equation in standard form set equal to zero. Then.

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,

Bell Problem Find the real number solutions of the equation: 18x 3 = 50x.

3.2 Polynomials-- Properties of Division Leading to Synthetic Division.

Dividing Polynomials Intro - Chapter 4.1. Using Long Division Example 1: Dividing Polynomials DIVISOR DIVIDEND REMAINDER QUOTIENT.

Do Now: Factor the following polynomial:. By the end of this chapter, you will be able to: - Identify all possible rational zeroes - Identify all actual.

7.5.1 Zeros of Polynomial Functions

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.

2.4 – Real Zeros of Polynomial Functions

Long Division Algorithm and Synthetic Division!!!

2.5 Apply the Remainder and Factor Theorems p. 120 How do you divide polynomials? What is the remainder theorem? What is the difference between synthetic.

5.4 – Apply the Remainder and Factor Theorems Divide 247 / / 8.

Polynomial Division and the Remainder Theorem Section 9.4.

Lesson 2.3 Real Zeros of Polynomials. The Division Algorithm.

6.5 The Remainder and Factor Theorems p. 352 How do you divide polynomials? What is the remainder theorem? What is the difference between synthetic substitution.

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

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.

 PERFORM LONG DIVISION WITH POLYNOMIALS AND DETERMINE WHETHER ONE POLYNOMIAL IS A FACTOR OF ANOTHER.  USE SYNTHETIC DIVISION TO DIVIDE A POLYNOMIAL BY.

The Remainder and Factor Theorems

The Remainder and Factor Theorems 6.5 p When you divide a Polynomial f(x) by a divisor d(x), you get a quotient polynomial q(x) with a remainder.

4-3 The Remainder and Factor Theorems

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley 4.3 Polynomial Division; The Remainder and Factor Theorems  Perform long division.

ACTIVITY 31: Dividing Polynomials (Section 4.2, pp )

6-7 The Division Algorithm & The Remainder Theorem dividend=quotient. divisor + remainder If a polynomial f(x) is divided by x - c, the remainder is the.

1. 2 Polynomial Function A polynomial function is a function of the form where n is a nonnegative integer and each a i (i = 0,1,…, n) is a real number.

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

4.3 The Remainder and Factor Theorems Objective: Find the factors of polynomials using the Remainder and Factor Theorems.

Textbook page 581 #’s 1, 2. Do Now – Example #1 Example 1: Divide 758 by 6 without a calculator using long division Identify: Dividend = ____________.

Dividing Polynomials Section 2.4. Objectives Divide two polynomials using either long division or synthetic division. Use the Factor Theorem to show that.

12/23/ Division and The Remainder Theorem.

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.

3.3 Polynomial and Synthetic Division. Long Division: Let’s Recall.

5.5 – Dividing Polynomials Divide 247 / / 8.

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

5-4 Dividing Polynomials Synthetic Division

Long and Synthetic Division. Long Division Polynomial long division can be used to divide a polynomial d(x), producing a quotient polynomial q(x) and.

Polynomial Synthetic Division

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

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.

Do Now: Divide Write out as much work as possible. Don’t divide in your head

Dividing Polynomials Two options: Long Division Synthetic Division.

Warm-ups Week 8 10/8/12 Find the zeros of f(x) = x3 + 2x2 – 13x + 10 algebraically (without a graphing calculator). What if I told.

Polynomial Division.

Dividing Polynomials A review of long division:

Dividing Polynomials.

Section 5.4 – Dividing Polynomials

Division of a Polynomial

Dividing Polynomials Long Division A little review:

4.3 Division of Polynomials

Polynomial Division; The Remainder Theorem and Factor Theorem

Polynomial Long Division

Division of Polynomials and the Remainder and Factor Theorems

5.5 Apply the Remainder and Factor Theorems

Long Division and Synthetic Division

6.5 The Remainder and Factor Theorems

The Remainder and Factor Theorems

Dividing Polynomials.

4.3 – The Remainder and Factor Theorems

Section 2.4: Real Zeros of Polynomial Functions

21 = P(x) = Q(x) . (x - r) + P(r) 4.3 The Remainder Theorem

Work on example #1 in today’s packet.

2.5 Apply the Remainder and Factor Theorem

5.5 Apply the Remainder and Factor Theorems

M3D14 Have out: Bellwork: pencil, red pen, highlighter, GP notebook

Presentation transcript:

Polynomial Long Division Algebraically finding the roots and factors of polynomials.

Remember…

Polynomials 𝑝(𝑥 𝑑(𝑥 =𝑞(𝑥)+ 𝑟(𝑥) d(𝑥) 𝑝(𝑥)=𝑞(𝑥)𝑑(𝑥)+𝑟(𝑥 We can do the same thing with polynomials. Let our first polynomial be p(x), our divisor (the one we are dividing by) be d(x), or quotient (answer) is q(x) and our remainder is r(x) then… ALSO 𝑝(𝑥 𝑑(𝑥 =𝑞(𝑥)+ 𝑟(𝑥) d(𝑥) 𝑝(𝑥)=𝑞(𝑥)𝑑(𝑥)+𝑟(𝑥

Example #1 - Find the quotient q(x) and the remainder r(x) if p(x) is divided by d(x). Write your answer in the form p(x)=q(x)d(x)+r(x): 𝑝(𝑥)= 𝑥 2 −11𝑥+30 𝑑(𝑥)=𝑥−3

Example #1 - Find the quotient q(x) and the remainder r(x) if p(x) is divided by d(x). Write your answer in the form p(x)=q(x)d(x)+r(x): 𝑝(𝑥)= 𝑥 2 −11𝑥+30 𝑑(𝑥)=𝑥−3 x -8 -3 x2 -11x +30 -x2 +3x ↓ -8x 8x -24 6

Note about Remainders When dividing, if the remainder is zero, that means that our divisor is a FACTOR of our dividend. Polynomial long division can be used to factor out complex polynomials.

Rational Roots Theorem Let f(x) be a polynomial. Then p/q is a potential zero of f(x) if: q is a factor of the leading coefficient and p is a factor of the constant term. p = Factors of the last term q = Factors of the first term

Example #2 – List the potential rational zeros of f(x).

Example #2 – List the potential rational zeros of f(x). ±

Assignment Polynomial Long Division Worksheet