5.3 – Polynomials and Polynomial Functions Definitions Coefficient: the numerical factor of each term. Constant: the term without a variable. Term: a number.

Slides:

Advertisements

Similar presentations

Section P4 Polynomials. How We Describe Polynomials.

Advertisements

Polynomials Identify Monomials and their Degree

Polynomials and Special Products

1 P.3 POLYNOMIALS Objectives:  Operations on polynomials  Applications of polynomials ( كثيرات الحدود )

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:

Day 1 – Polynomials Multiplying Mrs. Parziale

1.2 - Products Commutative Properties Addition: Multiplication:

Intermediate Algebra A review of concepts and computational skills Chapters 4-5.

EXPONENTS AND POLYNOMIALS College Algebra. Integral Exponents and Scientific Notation Positive and negative exponents Product rule for exponents Zero.

Section 5.1 Polynomials Addition And Subtraction.

Polynomials A monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents. The degree of a monomial.

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

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Exponents and Polynomials.

Drill #17 Simplify each expression.. Drill #18 Simplify each expression.

Polynomials P4.

Simplify Warm Up. Classifying Polynomials Section 8-1.

Introduction to Polynomials

1.2 - Products Commutative Properties Addition: Multiplication:

Adding & Subtracting Polynomials

Polynomials. The Degree of ax n If a does not equal 0, the degree of ax n is n. The degree of a nonzero constant is 0. The constant 0 has no defined degree.

 We use the acronym below to multiply two binomials. F – O – I – L – FIRST OUTSIDE INSIDE LAST.

7.6 Polynomials and Factoring Part 1: Polynomials.

How do you perform operations with polynomials? Section P4 (old text)

Sullivan Algebra and Trigonometry: Section R.4 Polynomials Objectives of this Section Recognize Monomials Recognize Polynomials Add, Subtract, and Multiply.

FHSPolynomials1 Vocabulary A monomial is a number, a variable, or a product of numbers and variables with whole number exponents. If the monomial includes.

13.01 Polynomials and Their Degree. A polynomial is the sum or difference of monomials. x + 3 Examples: Remember, a monomial is a number, a variable,

Polynomials Identify monomials and their degree Identify polynomials and their degree Adding and Subtracting polynomial expressions Multiplying polynomial.

Multiplying Polynomials *You must know how to multiply before you can factor!”

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals B.1 E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals.

Drill #29 Simplify each expression.. Drill #30 Simplify each expression.

10.6 – Special Products of Polynomials Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms.

Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.4 Polynomials.

3.2 Introduction to Polynomials. Identify Monomials Monomial or Term: An expression that is a constant or a product of a constant and variables that are.

Understanding Polynomials

6.1 Review of the Rules for Exponents

EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x – 3 ) Factor trinomial.

Polynomials Terms and Multiplying. Polynomial Term – number, variable or combination of the two, 2, x, 3y Polynomial – made up of 1 or more terms, separated.

Identifying Terms, Factors, and Coefficients (3.1.1) February 1st, 2016.

Chapter 5.1/5.2 Monomials and Polynomials. Vocabulary: A monomial is an expression that is a number, a variable, or the product of a number and one or.

Polynomials Objective: To review operations involving polynomials.

Polynomial – a monomial or sum of monomials Can now have + or – but still no division by a variable. MonomialBinomialTrinomial 13x 13x – 4 6x 2 – 5x +

Monomials An expression that is either a number, a variable, or a product of numerals and variables with whole number exponents.

Exponents and Monomials. Monomial is an expression that is a number, a variable, or a product of a number and variables. Constant is a monomial containing.

Polynomials and Polynomial Functions

Polynomials and Polynomial Functions

Objective - To factor trinomials in the form,

2.1 Classifying Polynomials

Polynomial Equations and Factoring

Aim: How do we multiply polynomials?

Introduction to Polynomials

Chapter 5 Polynomials.

Objective - To factor trinomials in the form .

Objective - To factor trinomials in the form,

Identifying Terms, Factors, and Coefficients (3.1.1)

Multiplying and Dividing Polynomials

Polynomials Monomials & Operations

Warm-up: Write in scientific notation: ,490,000

Introduction to Polynomials

Adding and subtracting

Objective - To factor trinomials in the form .

Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

Understanding polynomials

Only a life lived for others

Section P4 Polynomials.

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.

Only a life lived for others

Objective - To factor trinomials in the form .

Section 5.3 Polynomials and Polynomial Functions

Objective - To factor trinomials in the form,

Introduction to Polynomials

Presentation transcript:

5.3 – Polynomials and Polynomial Functions Definitions Coefficient: the numerical factor of each term. Constant: the term without a variable. Term: a number or a product of a number and variables raised to a power. Polynomial: a finite sum of terms of the form ax n, where a is a real number and n is a whole number.

Definitions Monomial: a polynomial with exactly one term. Binomial: a polynomial with exactly two terms. Trinomial: a polynomial with exactly three terms. 5.3 – Polynomials and Polynomial Functions

Definitions The Degree of a Term with one variable is the exponent on the variable. The Degree of a Term with more than one variable is the sum of the exponents on the variables. The Degree of a Polynomial is the greatest degree of the terms of the polynomial variables. 5.3 – Polynomials and Polynomial Functions

Practice Problems Identify the degrees of each term and the degree of the polynomial. 5.3 – Polynomials and Polynomial Functions

Practice Problems Evaluate each polynomial function 5.3 – Polynomials and Polynomial Functions

5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Monomials by Monomials Examples:

Multiplying Monomials by Polynomials Examples: 5.4 – Polynomials and Polynomial Functions Multiplication

Multiplying Two Polynomials Examples: 5.4 – Polynomials and Polynomial Functions Multiplication

5.4 – Multiplying Polynomials Special Products Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms

Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms 5.4 – Multiplying Polynomials Special Products

Squaring Binomials 5.4 – Multiplying Polynomials Special Products

Multiplying the Sum and Difference of Two Binomials 5.4 – Multiplying Polynomials Special Products

Dividing by a Monomial 5.4 – Multiplying Polynomials Special Products

Review of Long Division 6.4 – Dividing Polynomials Long Division

6.4 – Dividing Polynomials Long Division

6.4 – Dividing Polynomials Long Division

6.4 – Dividing Polynomials Long Division

5.7 - Factoring Polynomials Factoring Trinomials 20 is the result of the product of 4 and 5. 9 is the result of the sum of 4 and 5. Factors of 20 are:

Factoring Trinomials Factors of 24 are:1, 24 2, 12 3, 8 4, Factoring Polynomials

Factoring Trinomials Factors of 50 are:1, 50 2, 25 5, Factoring Polynomials

Factoring Trinomials Factors of 9 are: 1, 9 3, Factoring Polynomials

Factoring Trinomials Factors of 12 are: 1, 12 2,6 3, 4 Factors of 2 are: 1, Factoring Polynomials

Factoring Perfect Square Trinomials Not a perfect square Factoring Polynomials

Factoring Perfect Square Trinomials Factoring Polynomials

Factoring the Difference of Two Squares Not the difference Factoring Polynomials

Factoring the Difference of Two Squares Factoring Polynomials

Factoring the Sum or Difference of Two Cubes Factoring Polynomials

Factoring the Sum or Difference of Two Cubes Factoring Polynomials

Factoring the Sum or Difference of Two Cubes Factoring Polynomials

Factoring the Sum or Difference of Two Cubes Factoring Polynomials

End Of Presentation

Multiplying Two Polynomials Examples: 5.4 – Polynomials and Polynomial Functions Multiplication

Multiplying Two Polynomials Examples: 5.4 – Polynomials and Polynomial Functions Multiplication

Multiplying Two Polynomials Examples: 5.4 – Polynomials and Polynomial Functions Multiplication