REMAINDER THEOREM HONORS ADVANCED ALGEBRA PRESENTATION 2-7.

Slides:

Advertisements

Similar presentations

Notes 6.6 Fundamental Theorem of Algebra

Advertisements

7.4 Remainder and Factor Theorems 7.5 Roots and Zeros

Problem of the Day 1) I am thinking of four numbers such that

Rational Root Theorem.

2.7 Apply the Fundamental Theorem of Algebra day 2

Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function.

OBJECTIVES: 1. USE THE FUNDAMENTAL THEOREM OF ALGEBRA 2. FIND COMPLEX CONJUGATE ZEROS. 3. FIND THE NUMBER OF ZEROS OF A POLYNOMIAL. 4. GIVE THE COMPLETE.

Lesson 2.5 The Fundamental Theorem of Algebra. For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary.

5.7 Apply the Fundamental Theorem of Algebra

Academy Algebra II/Trig 5.5: The Real Zeros of a Polynomial Functions HW: p.387 (14, 27, 30, 31, 37, 38, 46, 51)

Complex Zeros; Fundamental Theorem of Algebra

9.9 The Fundamental Theorem of Algebra

Zeros of Polynomial Functions Section 2.5 Page 312.

PRE-AP PRE- CALCULUS CHAPTER 2, SECTION 5 Complex Zeros and the fundamental Theorem of Algebra.

The Rational Root Theorem.  Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST.

6.6 The Fundamental Theorem of Algebra

Ch 2.5: The Fundamental Theorem of Algebra

General Results for Polynomial Equations In this section, we will state five general theorems about polynomial equations, some of which we have already.

COMPLEX ZEROS: FUNDAMENTAL THEOREM OF ALGEBRA Why do we have to know imaginary numbers?

Section 3.3 Theorems about Zeros of Polynomial Functions.

Warm Up. Find all zeros. Graph.. TouchesThrough More on Rational Root Theorem.

Topic: U4L5 Remainder and Factor Theorems EQ: Can I correctly apply the Remainder and Factor Theorems to help me factor higher order polynomials?

2.5 The Fundamental Theorem of Algebra Students will use the fundamental theorem of algebra to determine the number of zeros of a polynomial. Students.

Fundamental Theorem of Algebra TS: Demonstrating understanding of concepts Warm-Up: T or F: A cubic function has at least one real root. T or F: A polynomial.

THE FUNDAMENTAL THEOREM OF ALGEBRA. Descartes’ Rule of Signs If f(x) is a polynomial function with real coefficients, then *The number of positive real.

3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have.

Remainder and Factor Theorems

THE LINEAR FACTORIZATION THEOREM. What is the Linear Factorization Theorem? If where n > 1 and a n ≠ 0 then Where c 1, c 2, … c n are complex numbers.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.6 Complex Zeros; Fundamental Theorem of Algebra.

1/27/ Fundamental Theorem of Algebra. Intro Find all zeros for each of the following: Multiplicity – When more than one zero occurs at the.

5.6 The Fundamental Theorem of Algebra. If P(x) is a polynomial of degree n where n > 1, then P(x) = 0 has exactly n roots, including multiple and complex.

January 19, 2012 At the end of today, you will be able to find ALL zeros of a polynomial. Warm-up: Check HW 2.4 Pg. 167 #20-21, 27-29, , 55, 65,

Section 4.6 Complex Zeros; Fundamental Theorem of Algebra.

7.5 Roots and Zeros Objectives:

2015/16 TI-Smartview 2.5 The Fundamental Theorem of Algebra.

The Fundamental Theorem of Algebra Intro - Chapter 4.6.

2.5 The Fundamental Theorem of Algebra. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra – If f(x) is a polynomial of degree n, where.

Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.

Honors Precalc: Warm-Up Solve for x. 1.) x = 0 2.)Perform the operation on the following complex numbers (express answers as a + bi). a.) (5 – 3i)(-2+4i)

Every polynomial P(x) of degree n>0 has at least one zero in the complex number system. N Zeros Theorem Every polynomial P(x) of degree n>0 can be expressed.

Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.

Algebra 2. Solve for x Algebra 2 (KEEP IN MIND THAT A COMPLEX NUMBER CAN BE REAL IF THE IMAGINARY PART OF THE COMPLEX ROOT IS ZERO!) Lesson 6-6 The Fundamental.

Roots & Zeros of Polynomials part 1

Fundamental Theorem of Algebra

College Algebra Chapter 3 Polynomial and Rational Functions

Roots and Zeros 5.7.

Solving Polynomial Functions

Complex Zeros Objective: Students will be able to calculate and describe what complex zeros are.

The Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

Rational Root and Complex Conjugates Theorem

Lesson 7.2: Finding Complex Solutions of Polynomial Equations

3.8 Complex Zeros; Fundamental Theorem of Algebra

Lesson 2.5 The Fundamental Theorem of Algebra

Finding Zeros of Polynomials

Lesson 2.5 The Fundamental Theorem of Algebra

5.7: Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra

4.6 - Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

College Algebra Chapter 3 Polynomial and Rational Functions

Apply the Fundamental Theorem of Algebra

Writing Polynomial Functions

Packet #9 Zeros of Polynomials

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra

Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts

Presentation transcript:

REMAINDER THEOREM HONORS ADVANCED ALGEBRA PRESENTATION 2-7

REMAINDER THEOREM

YOU TRY

APPLICATION OF FUNDAMENTAL THEOREM OF ALGEBRA The number of complex zeros is equal to the highest degree of the polynomial. This includes zeros with a mulitplicity greater than 1. The sum of imaginary and real zeros always totals the number of complex zeros. The number of possible imaginary zeros is a multiple of 2 because imaginary zeros always come in conjugate pairs. The number of possible real zeros is equal to the number of total zeros decreased by a multiple of 2.

EXAMPLE

YOU TRY