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.

Slides:

Advertisements

Similar presentations

Plowing Through Sec. 2.4b with Two New Topics: Homework: p odd Remainder and Factor Theorems with more Division Practice.

Advertisements

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

2.4 – Zeros of Polynomial Functions

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,

Section 5.5 – The Real Zeros of a Rational Function

Dividing Polynomials; Remainder and Factor Theorems.

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.)

2.2 Remainder and Factor Theorems 1 Remainder Theorem If the polynomial f(x) is divided by x  c, then the remainder is equal to f(c). In other words,

Limit Laws Suppose that c is a constant and the limits lim f(x) and lim g(x) exist. Then x -> a Calculating Limits Using the Limit Laws.

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.

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

Section 2.3 Polynomial and Synthetic Division Long Division of polynomials Ex. (6x 3 -19x 2 +16x-4) divided by (x-2) Ex. (x 3 -1) divided by (x-1) Ex (2x.

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.

Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.

Factors, Remainders, and Roots, Oh My! 1 November 2010.

The Remainder and Factor Theorems

7.4 THE REMAINDER & FACTOR THEOREMS Objectives: The student will be able to… 1)evaluate functions using synthetic substitution 2)determine whether a binomial.

Do Now Let 1. Which of the given polynomials is a factor of f(x)?

Section 2.4 Dividing Polynomials; The Factor and Remainder Theorems.

2.3 Polynomial Division and Synthetic Division Ex. Long Division What times x equals 6x 3 ? 6x 2 6x x 2 Change the signs and add x x.

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

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.

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.

UNIT 2, LESSON 4 THEOREMS ABOUT ZEROS. GETTING STARTED Find the quotient and remainder when is divided by x-3.

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

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

I CAN USE LONG DIVISION AND SYNTHETIC DIVISION. I CAN APPLY THE FACTOR AND REMAINDER THEOREMS. Lesson 2-3 The Remainder and Factor Theorems.

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.

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.

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

Dividing Polynomials Section 4.3.

Dividing Polynomials Two options: Long Division Synthetic Division.

Warm Up Compute the following by using long division.

Chapter 6 More about Polynomials

Homework Questions?.

Section 3.2 Dividing Polynomials (std Alg 2 3.0)

Divide by x - 1 Synthetic Division: a much faster way!

4.4 Rational Functions A Rational Function is a function whose rule is the quotient of two polynomials. i.e. f(x) = 1

3.7 The Real Zeros of a Polynomial Function

Remainder and Factor Theorems

The Remainder and Factor Theorems

Aim: What are the remainder and factor theorem?

Long & Synthetic Division

Dividing Polynomials Long Division A little review:

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

7.4 The Remainder and Factor Theorems

Packet #8 Dividing Polynomials

IF c is constant and lim f(x) and lim g(x) exist then…

Apply the Remainder and Factor Theorems

Polynomial Division; The Remainder Theorem and Factor Theorem

A POLYNOMIAL is a monomial or a sum of monomials.

3.7 The Real Zeros of a Polynomial Function

Homework Questions?.

Remainder and Factor Theorem

What is synthetic division?

Long Division and Synthetic Division

The Factor Theorem A polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

What is synthetic division?

The Remainder and Factor Theorems

1.2 Analyzing Graphs of Functions and Relations

3.6 Polynomial Functions Part 2

What is synthetic division?

What is synthetic division?

The Remainder and Factor Theorems

Section 2.4: Real Zeros of Polynomial Functions

What is synthetic division?

Dividing Polynomials (SYNTHETIC Division)

Presentation transcript:

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

Find the remainder when f(x) is divided by g(x) without using division. 2. f(x) = x5 - 10x4 + 20x3 – 5x - 95; g(x) = x + 10

Factor Theorem: A polynomial function f(x) has a linear factor x – a if and only if f(a) = 0. That means…plug a into function, evaluate & if the remainder is ZERO then x – a is a FACTOR.

Use the factor to determine whether h(x) is a factor of f(x). 3. h(x) = x – 3; f(x) = x3 - 4x2 + 2x + 3 4. h(x) = x + 2; f(x) = x3 + x2 – 4x + 4