Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.3 Introduction to Polynomials.

Slides:



Advertisements
Similar presentations
Section P4 Polynomials. How We Describe Polynomials.
Advertisements

Adding and Subtracting Polynomials
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Rational Expressions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 3 Exponents and Polynomials.
Factoring Polynomials
5.3 – Polynomials and Polynomial Functions Definitions Coefficient: the numerical factor of each term. Constant: the term without a variable. Term: a number.
10.1 – Exponents Notation that represents repeated multiplication of the same factor. where a is the base (or factor) and n is the exponent. Examples:
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.2 Factoring Trinomials of the Form x 2 + bx + c.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 10 Exponents and Polynomials.
Chapter 5 Section 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Exponents and Polynomials.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.5 Multiplying Polynomials.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Exponents and Polynomials.
Polynomial Functions and Adding and Subtracting Polynomials
Lesson 8-1 Warm-Up.
Simplify Warm Up. Classifying Polynomials Section 8-1.
Introduction to Polynomials
World 1-2 Adding and Subtracting Polynomials. Recall; A monomial is a single algebraic term A binomial contains two unlike terms A trinomial has 3 unlike.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.7 Dividing Polynomials.
Exponents and Polynomials Chapter Ten Adding and Subtracting Polynomials Section 10.1.
Adding & Subtracting Polynomials
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.3 Further Solving Linear Equations.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.4 Factoring Trinomials of the Form ax 2 + bx + c by Grouping.
Polynomials and Polynomial Functions
Chapter 4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 4-1 Exponents and Polynomials.
Section 9-1 Adding and Subtracting Polynomials SPI 12C: add and subtract algebraic expressions Objectives: Classify a polynomial by degree and number of.
Chapter 5 Polynomials: An Introduction to Algebra.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.4 Adding and Subtracting Rational Expressions with Different Denominators.
Martin-Gay, Intermediate Algebra: A Graphing Approach, 4ed 1 § 5.2 More Work with Exponents and Scientific Notation.
Polynomials. Polynomial Term Binomial Trinomial 1 or more monomials combined by addition or subtraction each monomial in a polynomial polynomial with.
Section 2Chapter 5. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 Adding and Subtracting Polynomials Know the basic definitions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.8 Solving Equations Containing Fractions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 3 Solving Equations and Problem Solving.
Adding and Subtracting Polynomials
Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.4 Polynomials.
OBJECTIVES: 1) TO EVALUATE POLYNOMIAL FUNCTIONS. 2) TO SIMPLIFY POLYNOMIALS BY COLLECTING LIKE TERMS. PDN: SIMPLIFY. 1)X²X³= 2)(X³Y²)(XY)= 5-1 Polynomials.
Understanding Polynomials
5-1 Monomials Objectives Multiply and divide monomials
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.5 Multiplying Whole Numbers and Area.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 2.3 Subtracting Integers.
Polynomial Degree and Finite Differences Objective: To define polynomials expressions and perform polynomial operations.
Martin-Gay, Beginning Algebra, 5ed 22 x x 3 2  x 5 2  x + 11 Polynomial Vocabulary Term – a number or a product of a number and variables raised.
Add and Subtract Polynomials Lesson 9.1 OBJ: to add and subtract polynomials.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.3 Solving Linear Equations in One Variable.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Real Numbers and Introduction to Algebra.
Monomials An expression that is either a number, a variable, or a product of numerals and variables with whole number exponents.
Adding and subtracting polynomials 1L interpret expressions that represent a quantity in terms of its context.
SECTION 2.6 ADDING AND SUBTRACTING EXPRESSIONS OBJECTIVES: USE THE DISTRIBUTIVE PROPERTY TO COMBINE LIKE TERMS AND SIMPLIFY EXPRESSIONS WITH SEVERAL VARIABLES.
Polynomials and Polynomial Functions
Polynomials and Polynomial Functions
In this lesson we will classify, add and subtract polynomials.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Polynomial Functions and Adding and Subtracting Polynomials
8-1 Adding and Subtracting Polynomials
Lesson 4.1 Understanding Polynomial Expressios
Introduction to Polynomials
Adding and Subtracting Polynomials
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Polynomials Monomials & Operations
Adding and Subtracting Polynomials
4.1 Introduction to Polynomials Objectives:
4.1 Introduction to Polynomials Objectives:
7-5 Polynomials Lesson Presentation Lesson Quiz Holt Algebra 1.
Introduction to Polynomials
Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.
7-5 Polynomials Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1.
5.5 Polynomials Goals: To identify terms, coefficients, and factors of a term. To simplify a poly by collecting like terms To identify the degree of the.
Do Now: Aim: How do we work with polynomials?
Presentation transcript:

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.3 Introduction to Polynomials

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Defining Term and Coefficient Term – a number or a product of a number and variables raised to powers Coefficient – numerical factor of a term Constant – term which is only a number Polynomial is a finite sum of terms of the form ax n, where a is a real number and n is a whole number.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. In the polynomial 7x 5 + x 2 y 2 – 4xy + 7 There are 4 terms: 7x 5, x 2 y 2, – 4xy and 7. The coefficient of term 7x 5 is 7, of term x 2 y 2 is 1, of term –4xy is –4 and of term 7 is 7. 7 is a constant term. Defining Term and Coefficient

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Monomial is a polynomial with exactly one term. Binomial is a polynomial with exactly two terms. Trinomial is a polynomial with exactly three terms. Types of Polynomials

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The degree of a term in one variable is the exponent on the variable. The degree of a constant is 0. The degree of a polynomial is the greatest degree of any term of the polynomial. The degree of 9x 3 – 4x is 3. The degree of a term with more than one variable is the sum of the exponents on the variables. The degree of the term 5a 4 b 3 c is 8 (remember that c can be written as c 1 ). Degrees

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Evaluating a polynomial for a particular value involves replacing the value for the variable(s) involved. Find the value of 2x 3 – 3x + 4 when x = – 2. = 2( – 2) 3 – 3( – 2) + 42x 3 – 3x + 4 = 2( – 8) = – 6 Evaluating Polynomials Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Like terms are terms that contain exactly the same variables raised to exactly the same powers. Combine like terms to simplify. x 2 y + xy – y + 10x 2 y – 2y + xy Only like terms can be combined through addition and subtraction. Warning! = 11x 2 y + 2xy – 3y = (1 + 10)x 2 y + (1 + 1)xy + (– 1 – 2)y = x 2 y + 10x 2 y + xy + xy – y – 2y Group like terms. Combining Like Terms Example Use the distributive property. Simplify.