 What is a zero?  What ways do you know to find a zero?

Slides:



Advertisements
Similar presentations
5.5: Polynomial Long Division and Synthetic Division
Advertisements

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,
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.
Zeros of Polynomial Functions
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.
Polynomial Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Polynomial Function A polynomial function is.
EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.
Finding Rational Zeros.
2.3 Synthetic Substitution
A3 3.4 Zeros of Polynomial Functions Homework: p eoo, odd.
Chapter 2 Polynomial and Rational Functions. Warm Up 2.3  An object is launched at 19.6 meters per second from a meter tall platform. The equation.
Obj: To solve equations using the Rational Root Theorem.
Finding the Potential Zeros.  A Theorem that provides a complete list of possible Rational Roots or Zeroes of the Polynomial Equation.  A Root or Zero.
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.
Chapter 8 Summary. Direct Variation If y = kx, then y is said to vary directly as x or be directly proportional to x. – K is the constant of variation.
2.3 Synthetic Substitution OBJ:  To evaluate a polynomial for given values of its variables using synthetic substitution.
Rational Root Theorem By: Yu, Juan, Emily. What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.
7.5.1 Zeros of Polynomial Functions
Using Technology to Approximate Roots of Polynomial Equations.
Finding Real Roots of Polynomial Equations
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.
Real Zeros of Polynomial Functions. Quick Review.
Copyright © 2009 Pearson Education, Inc. CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions.
Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.
Warm Up. Algebra 3 Chapter 7: Powers, Roots, and Radicals Lesson 3: Power Functions and Function Operations.
Section 5.5 The Real Zeros of a Polynomial Function.
2.4/2.52.4/2.5 Real Zeros of Polynomial Functions.
The Remainder Theorem A-APR 2 Explain how to solve a polynomial by factoring.
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.
Warm Up. Algebra 3 Chapter 6 Lesson 4 Factoring and Solving Polynomial Equations.
3.3 Polynomial and Synthetic Division. Long Division: Let’s Recall.
Finding Rational Zeros (Day 1)
6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a.
Used to factor polynomials when no other method works.
LESSON 5.6 Rational Zeros of Polynomial Functions.
Warm Up. Algebra 3 Chapter 6 Lesson 4 Factoring and Solving Polynomial Equations.
The Real Zeros of a Polynomial Function Section 5.2 Also Includes Section R.6 : Synthetic Division 1.
The Remainder Theorem & The Factor Theorem Section 3.1.
9.8 Day 2 – Finding Rational Zeros. The Rational Zero Theorem: If has integer coefficients, then every rational zero of f have the following form:
Section 3.4 – Zeros of a Polynomial. Find the zeros of 2, -3 (d.r), 1, -4.
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.
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.
Rational Zero Theorem Used to factor a cubic or quartic polynomial function with a leading coefficient not equal to 1.
Polynomial Synthetic Division
Polynomial Long Division
Mrs. Shahmoradian (Ms. Tanskley) Monday 2nd.  Answer the following questions about the Polynomial equation: 6x^3 + 8x^2 – 7x – 3 = 0 1) How many roots.
Zeros (Solutions) Real Zeros Rational or Irrational Zeros Complex Zeros Complex Number and its Conjugate.
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.
Goal: to divide polynomials using LONG and SYNTHETIC methods.
Polynomial Long Division Review
Pre-Calculus Section 2.3 Synthetic Division
Long & Synthetic Division
7.4 The Remainder and Factor Theorems
2.3 Notes: Polynomial and Synthetic Division
2.5 Zeros of Polynomial Functions
Real Zeros Intro - Chapter 4.2.
5.6 Find The Rational Zeros
Polynomial Long Division Review
Warm Up #2 Factor completely. 2. 2x2 – 5x – 3 1. x2 – x – 12
Remainder and Factor Theorem
Notes Over 6.6 Possible Zeros Factors of the constant
Digital Lesson Polynomial Functions.
Zeros of polynomial functions
Section 2.4: Real Zeros of Polynomial Functions
Digital Lesson Polynomial Functions.
Warm Up.
Dividing Polynomials (SYNTHETIC Division)
Presentation transcript:

 What is a zero?  What ways do you know to find a zero?

 Use the rational zero theorem to find all possible zeros

 WRITE THE PROBLEM IN STANDARD FORM  DOESN’T need missing terms  Look at the constant  Factor it  Look at the leading coefficient  Factor it  LIST ALL COMBINATIONS  All answers have a plus/minus

 Today we learned how to find all possible zeros using the rational zero theorem

 Worksheet  6.6B (1 – 3)

 We will find all real zeros of a polynomial

 Find all possible zeros using RZT (yesterday)  Plug your answers into synthetic division  If your remainder is zero then it’s a REAL zero  If your remainder isn’t then it is NOT a real zero  Once you find an answer remember to take the opposite for the equation  Example -2 means I write x + 2  Example 3/4 means I write 4x - 3

 Find all possible zeros using RZT (yesterday)  Plug your answers into the equation using direct substitution for the x  Once you find an answer that equals zero remember to take the opposite for the equation  Example -2 means I write x + 2  Example 3/4 means I write 4x - 3

 We will find all real zeros of a polynomial

 In your calculator  Type the problem into y=  Then you can either use the table  Or use the graph and find the zeros

 Today we learned how to find all REAL zeros of a polynomial

 Worksheet  6.6B ( )