Coefficient: a number multiplied by a variable.. Degree: the greatest exponent of its variable.

Slides:

Advertisements

Similar presentations

Notes 6.6 Fundamental Theorem of Algebra

Advertisements

Chapter 6 – Polynomial Functions

Dividing Polynomials.

Chapter 2 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Dividing Polynomials: Remainder and Factor Theorems.

Zeros of Polynomial Functions Section 2.5. Objectives Use the Factor Theorem to show that x-c is a factor a polynomial. Find all real zeros of a polynomial.

2.5 Zeros of Polynomial Functions

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Chapter 4 – Polynomials and Rational Functions

Bell Problem Find the real number solutions of the equation: 18x 3 = 50x.

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.

The Fundamental Theorem of Algebra And Zeros of Polynomials

1 Polynomial Functions Exploring Polynomial Functions Exploring Polynomial Functions –Examples Examples Modeling Data with Polynomial Functions Modeling.

6.1 Using Properties of Exponents What you should learn: Goal1 Goal2 Use properties of exponents to evaluate and simplify expressions involving powers.

Dividing Polynomials Intro - Chapter 4.1. Using Long Division Example 1: Dividing Polynomials DIVISOR DIVIDEND REMAINDER QUOTIENT.

Bell Ringer 1. What is the Rational Root Theorem (search your notebook…Unit 2). 2. What is the Fundamental Theorem of Algebra (search your notebook…Unit.

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

Lesson 4-1 Polynomial Functions.

4-5, 4-6 Factor and Remainder Theorems r is an x intercept of the graph of the function If r is a real number that is a zero of a function then x = r.

3.3: Dividing Polynomials: Remainder and Factor Theorems Long Division of Polynomials 1.Arrange the terms of both the dividend and the divisor in descending.

Notes 2.4 –Real Zeros of Polynomial Functions

Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.

Chapter 3 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Zeros of Polynomial Functions.

An Introduction to Polynomials

Algebra 2.  Warm Up  A monomial is an expression that is either a real number, a variable or a product of real numbers and variables.  A polynomial.

 Evaluate a polynomial  Direct Substitution  Synthetic Substitution  Polynomial Division  Long Division  Synthetic Division  Remainder Theorem 

Chapter 9 Polynomial Functions

Long Division Algorithm and Synthetic Division!!!

Today in Pre-Calculus Go over homework Notes: Remainder and Factor Theorems Homework.

Zeros of Polynomials 2.5.

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

Introduction Synthetic division, along with your knowledge of end behavior and turning points, can be used to identify the x-intercepts of a polynomial.

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

4.5 Quadratic Equations Zero of the Function- a value where f(x) = 0 and the graph of the function intersects the x-axis Zero Product Property- for all.

Polynomials and End Behavior

Chapter 1 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Dividing Polynomials; Remainder and Factor Theorems.

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.

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.

3.3 Polynomial and Synthetic Division. Long Division: Let’s Recall.

7.5 Roots and Zeros Objectives: The student will be able to…

Remainder and Factor Theorems

Get out your homework, but keep it at your desk..

Objectives: Students will be able to… Determine the number of zeros of a polynomial function Find ALL solutions to a polynomial function Write a polynomial.

Solving Polynomials.

Polynomial Division Objective: To divide polynomials by long division and synthetic division.

College Algebra Chapter 3 Polynomial and Rational Functions Section 3.3 Division of Polynomials and the Remainder and Factor Theorems.

Zeros of Polynomial Functions A-APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is.

Quadratic Function A quadratic function is defined by a quadratic or second-degree polynomial. Standard Form

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

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

Polynomials and Polynomial Functions

3.4 Zeros of Polynomial Functions

Bell Ringer 1. What is the Rational Root Theorem

Algebra II with Trigonometry Ms. Lee

Aim #3. 3 How do we divide Polynomials

Power and Polynomial Functions

4-1 Polynomial Functions

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Finding Zeros of Polynomials

Today in Precalculus Go over homework Notes: Remainder

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

3.3 Zeros of Polynomials.

Algebra 2/Trigonometry Name: __________________________

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

3.6 Polynomial Functions Part 2

Algebra 2/Trigonometry Name: __________________________

4.1: Polynomial Functions

Apply the Fundamental Theorem of Algebra

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

5.8 Analyzing Graphs of Polynomials

Presentation transcript:

Coefficient: a number multiplied by a variable.

Degree: the greatest exponent of its variable

End Behavior: the value of f(x) as x approaches positive and negative infinity

Fundamental Theorem of Algebra: every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity.

Multiplicity: the number of times a root occurs at a given point of a polynomial equation.

Pascal’s Triangle: an arrangement of the values n Cr of in a triangular pattern where each row corresponds to a value of n

Relative Minimum: a point on the graph where the function is increasing as you move away from the point in the positive and negative direction along the horizontal axis.

Relative Maximum: a point on the graph where the function is decreasing as you move away from the point in the positive and negative direction along the horizontal axis.

Remainder Theorem: states that the remainder of a polynomial f(x) divided by a linear divisor (x – c) is equal to f(c).

Roots: solutions to polynomial equations.

Synthetic Division: Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form (x – a). It can be used in place of the standard long division algorithm.

Zero: If f(x) is a polynomial function, then the values of x for which f(x) = 0 are called the zeros of the function. Graphically, these are the x intercepts.