Section 2-5 Zeros of Polynomial Functions. 1. Find all the zeros of and write the polynomial as a product of linear factors.

Slides:



Advertisements
Similar presentations
Notes 6.6 Fundamental Theorem of Algebra
Advertisements

Copyright © Cengage Learning. All rights reserved.
EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES
2.8 Analyzing Graphs of Polynomial Functions p. 373
Zeros of Polynomial Functions
Section 5.4 Dividing Polynomials. Review of Long Division What terms do we use to describe 672 and 21? Because the reminder is zero, we know that 21 is.
Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.
Section 5.5 – The Real Zeros of a Rational Function
Zeros of Polynomial Functions
Polynomial Functions and Models Section 5.1. Polynomial Functions.
Polynomial and Rational Functions
5.8 Rational Zero Theorem. T HE R ATIONAL Z ERO T HEOREM : If f(x) = a n x n + a n-1 x n-1 + a n-2 x n-2 + … + a 1 x 1 + a 0 has integer coefficients,
Volume word problems Part 2.
 Find a polynomial with specified zeros.  For a polynomial function with integer coefficients, find the rational zeros and the other zeros, if possible.
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.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 5–7) CCSS Then/Now Key Concept: Rational Zero Theorem Example 1:Identify Possible Zeros Example.
6.8 Analyzing Graphs of Polynomial Functions
Objectives I will use the distributive property to factor a polynomial.
Splash Screen. Concept Example 1 Identify Possible Zeros A. List all of the possible rational zeros of f(x) = 3x 4 – x Answer:
Factor and Solve Polynomial Equations 2.3 (GREEN book) Polynomial Review WS: due TOMORROW.
Graphing Polynomials. Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum.
UNIT 2, LESSON 1 POLYNOMIAL FUNCTIONS. WHAT IS A POLYNOMIAL FUNCTION? Coefficients must be real numbers. Exponents must be whole numbers.
Polynomial Functions and Models
Factor completely. 1. x2 – x – 12 ANSWER (x – 4)(x + 3)
Factor and Solve Polynomial Equations 2.3 (GREEN book)
Section 3.4 – Zeros of a Polynomial. Find the zeros of 2, -3 (d.r), 1, -4.
Polynomial P(x) Linear Factors Solutions of P(x)=0 Zeros of P(x) P(x) = 0.
6.6: FINDING RATIONAL ZEROS Objectives: Students will be able to… Find all real zeros of a polynomial function Use the rational zero test to determine.
What is a polynomial function of least degree with integral coefficients the zeros of which include 2 and 1 + i? 1.According to the Complex Conjugate Theorem,
Remainder Theorem Section 6-3b. Remainder Theorem.
Chapter 5 Section 4. EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x.
Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.
6.3 Dividing polynomials.
Welcome to Precalculus!
Section 10.8 Factoring Using the Distributive Property
Name:__________ warm-up 5-8
EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES
Conjugate Pairs Let f (x) is a polynomial function that has real
Quiz.
Copyright © Cengage Learning. All rights reserved.
Analyzing Graphs of Polynomial Functions
Notes Over 3.4 The Rational Zero Test
4.4 The Rational Root Theorem
Warm-up Multiply the factors and write in standard form.
2.5(c) Notes: Zeros of Polynomial Functions
Real Zeros Intro - Chapter 4.2.
Rational Zero Theorem Rational Zero Th’m: If the polynomial
7.5 Zeros of Polynomial Functions
7.1: Finding Rational Solutions of Polynomial Equations
7.5 Zeros of Polynomial Functions
Zeros of Polynomial Functions
WARM UP Factor the polynomial completely. b b2
Notes 5.6 (Day 1) Find Rational Zeros.
Section 3.4 Zeros of Polynomial Functions
4.4 The Rational Root Theorem
6.8 Analyzing Graphs of Polynomial Functions
Zeros of a Polynomial Function
The Fundamental Theorem of Algebra
Parent Functions.
Splash Screen.
Parent Functions.
Fundamental Theorem of Algebra
2.5 The Real Zeros of a Polynomial Function
Notes Over 6.6 Possible Zeros Factors of the constant
Polynomial and Rational Functions
Zeros of polynomial functions
The Real Zeros of a Polynomial Function
The Real Zeros of a Polynomial Function
Splash Screen.
Presentation transcript:

Section 2-5 Zeros of Polynomial Functions

1. Find all the zeros of and write the polynomial as a product of linear factors.

2. Find the rational zeros of

3. Find the rational zeros of

4. Find the rational zeros of

5. Find all the real zeros of

6. Find a polynomial function with integer coefficients that has and as zeros.

7. Find all the zeros of given that 4i is a zero of f.

8. Write as the product of linear factors, and list all of its zeros.

9. Describe the possible real zeros of

10. Find the real zeros of

Suppose each candle-making kit contains 147 cubic inches of candle wax and a mold for making the pyramid-shaped candle. You want the height of the candle to be 2 inches more than the length of each side of the candle's square base. What should the dimensions of your candle mold be?