5.6 – Find the Rational Zeros

Slides:

Advertisements

Similar presentations

4.4 Rational Root Theorem.

Advertisements

Notes 6.6 Fundamental Theorem of Algebra

Bell Problem Factor the polynomial completely given that x – 4 is a factor: f(x) = x3 – x2 – 22x + 40.

2.4 – Zeros of Polynomial Functions

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

Section 5.5 – The Real Zeros of a Rational Function

OBJECTIVE: I will be able to calculate the real zeros of a polynomial function using synthetic division and the Rational Zero Theorem through use of in-class.

Objective Video Example by Mrs. G Give It a Try Lesson 6.6  Find the rational and real zeros of a polynomial function.

5.6 Notes: Find Rational Zeros. Rational Zeros: Where the graph crosses the x-axis at a rational number Rational Zero Theorem: To find the possible rational.

Mrs. McConaughy Honors Algebra 2 1 Lesson 6.5: Finding Rational Zeros Objective: To find the rational zeros of a polynomial function.

Finding Real Roots of Polynomial Equations

Splash Screen. Example 1 Identify Possible Zeros A. List all of the possible rational zeros of f(x) = 3x 4 – x Answer:

Homework Lesson 2.3 Read: Pages Page 127: #1-61 (EOO)

7.6 Rational Zero Theorem Algebra II w/ trig. RATIONAL ZERO THEOREM: If a polynomial has integer coefficients, then the possible rational zeros must be.

Chapter 2 Polynomial and Rational Functions. Warm Up

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

The Real Zeros of a Polynomial Function Obj: Apply Factor Theorem, Use Rational Zero Theorem to list roots, Apply Descartes’ Rule of Signs to determine.

Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.

Real Zeros of Polynomials Section 2.4. Review – Long Division 1. What do I multiply by to get the first term? 2. Multiply through 3. Subtract 4. Bring.

7.6 Rational Zero Theorem Objectives: 1. Identify the possible rational zeros of a polynomial function. 2. Find all the rational zeros of a polynomial.

Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.

LESSON 5.6 Rational Zeros of Polynomial Functions.

Real Zeros of Polynomial Functions. Solve x 3 – 2x + 1 = 0. How? Can you factor this? Can you use the quadratic formula? Now what if I tell you that one.

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.

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.

Precalculus Lesson 2.5 The Fundamental Theorem of Algebra.

Examples Rational Zero Theorem For the following polynomials, list all of the possible real zeroes. Do not forget the  ’s. 1. x x x

EXAMPLE 1 List possible rational zeros List the possible rational zeros of f using the rational zero theorem. a. f (x) = x 3 + 2x 2 – 11x + 12 Factors.

TRASHKETBALL PRECALCULUS CHAPTER 2 QUIZ. WHAT IS THE VERTEX AND WHAT ARE THE INTERCEPTS?

Lesson 2.2 Read: Pages Page 112: #1-9 (EOO), (EOO), (EOO)

Term 1 Week 8 Warm Ups. Warm Up 9/28/15 1.Graph the function and identify the number of zeros: 2x 3 – 5x 2 + 3x – 2 (Hit the y = ) 2.Identify the expressions.

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

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.

Warm Up Compute the following by using long division.

Algebra II 5.6: Find Rational Zeros HW tonight: p.374 (4-10 even)

Descartes Rule of Signs Positive real zeros = Negative real zeros =

Copyright © Cengage Learning. All rights reserved.

Notes Over 3.4 The Rational Zero Test

Locating Real Zeros of Polynomials

2.5 Zeros of Polynomial Functions

Real Zeros Intro - Chapter 4.2.

Rational Zero Theorem Rational Zero Th’m: If the polynomial

Finding Real Roots of Polynomial Equations

3.8 Complex Zeros; Fundamental Theorem of Algebra

Rational Root Theorem Math 3 MM3A1.

Finding polynomial roots

5.6 Find Rational Zeros.

Notes 5.6 (Day 1) Find Rational Zeros.

1.) Algebra 2/Trigonometry Name: ________________

Zeros of a Polynomial Function

List all possible rational zeros given by the rational zeros theorem (but don't check to see which actually are zeros). {image} Choose the answer.

Warm-up: Sketch the graph of f(x) = x5 – 4x4 + 4x3. Be sure to include all critical values. HW: Quiz Review 2.1/2.2.

Graphing Polynomials Unit 1D Day 19.

Lesson 5.8 Graphing Polynomials.

Problem of the day.

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

Fundamental Theorem of Algebra

2.5 The Real Zeros of a Polynomial Function

The Real Zeros of a Polynomial Function

Fundamental Theorem of Algebra

Notes Over 6.6 Possible Zeros Factors of the constant

8-5 Rational Zero Theorem

Zeros of polynomial functions

2.6 Find Rational Zeros Pg. 89.

Section 2.4: Real Zeros of Polynomial Functions

2.6 Find Rational Zeros Pg. 89.

Preview to 6.7: Graphs of Polynomial

Bellwork Solve the Polynomial Equation by Factoring

The Real Zeros of a Polynomial Function

Presentation transcript:

5.6 – Find the Rational Zeros

5.6 – Find the Rational Zeros Example 1: List the possible rational zeros of f using the rational zero theorem. f(x) = x3+ 2x2 – 11x + 12 f(x) = 4x4 – x3 – 3x2 + 9x - 10

5.6 – Find the Rational Zeros Verifying Zeros In Lesson 5.5, you found zeros of polynomial functions when one zero was known. The rational zero theorem is a starting point to find zeros when NO zeros are known. However, the rational zero theorem lists only possible zeros. In order to find the actual zeros of a polynomial function f, you must test values from the list of possible zeros.

5.6 – Find the Rational Zeros Example 2: Find all real zeros of f(x) = x3 – 8x2 + 11x + 20

5.6 – Find the Rational Zeros Example 2b: Find all real zeros of f(x) = x3 – 5x2 + 7x – 35

5.6 – Find the Rational Zeros Limiting the search for zeros In the previous examples, the leading coefficient of the polynomial is 1. When the leading coefficient is not 1, the list of possible rational zeros can increase dramatically. In such cases, the search can be shortened by sketching the function’s graph.

5.6 – Find the Rational Zeros Example 3: Find all real zeros of f(x) = 10x4 – 11x3 – 42x2 + 7x + 12