Classifying Polynomials

Slides:

Advertisements

Similar presentations

Polynomials By the end of class, you will be able to:

Advertisements

1.Be able to determine the degree of a polynomial. 2.Be able to classify a polynomial. 3.Be able to write a polynomial in standard form.

5.5 Polynomials Goals: 1. To identify a polynomial and its types 2.To identify terms, coefficients 3.To identify the degree of the poly.

Section 4.2 Adding & Subtracting Polynomials. Monomial An expression that is either a numeral, a variable, or a product of a numeral and one or more variables.

Polynomials Objective: find the degree of a polynomial. Arrange the terms of a polynomial in ascending or descending order.

Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x ) -(x – 6) Simplify each expression. 4) (x + 5)

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.

Warm Up. Intro to Polynomials Definition A polynomial is a sum of terms containing the same variable raised to different powers.

Chapter 9 Polynomials. What are polynomials? Poly- nomial- What are monomials Mono- nomial.

Objectives The student will be able to: 1. find the degree of a polynomial. 2. arrange the terms of a polynomial in ascending or descending order. SOL:

Objectives The student will be able to: LEARN ABOUT EXPONENTS AND ADD AND SUBTRACT POLYNOMIALS MATH 8A.

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,

8.4 Polynomials Find the degree of a polynomial. Arrange the terms of a polynomial in ascending or descending order.

Adding and subtracting Polynomials Lesson 8-1 TOPIC IX: Quadratic Equations and Functions.

4.1 Introduction to Polynomials. Monomial: 1 term (ax n with n is a non- negative integers, a is a real number) Ex: 3x, -3, or 4xy 2 z Binomial: 2 terms.

Objectives The student will be able to: 1. find the degree and leading coefficient of a polynomial. 2.arrange the terms of a polynomial in ascending or.

Polynomials Algebra I. Remember: Monomials are separated by______ or ______ signs. Monomial = One term – A number, a variable, or a product of numbers.

4.3 Polynomials. Monomial: 1 term (ax n with n is a non- negative integers) Ex: 3x, -3, or 4y 2 Binomial: 2 terms Ex: 3x - 5, or 4y 2 + 3y Trinomial:

Lesson 8-4 Polynomials. Definitions Polynomial- a monomial or a sum of monomials. Binomial- the sum of two monomials. Trinomial- the sum of three monomials.

Addition and Subtraction of Polynomials.  A Polynomial is an expression comprised of one or more terms. Terms are separated by + or – (Polynomials are.

Understanding Polynomials

Chapter 4 Working with Polynomials Important Terms.

Polynomials Polynomials  Examples : Monomials: 4f 3x 3 4g 2 2 Binomials: 4t – 7g 5x 2 + 7x 6x 3 – 8x Trinomials: x 2 + 2x + 3 5x 2 – 6x.

Adding and subtracting polynomials. 5x 3 + 2x 2 – x – 7 5x 3 + 2x 2 – x – 7 This is a polynomial in standard form: Leading Coefficient Degree Constant.

WARM UP (4x 4 y 3 ) Objectives The student will be able to: 1. find the degree of a polynomial. 2. arrange the terms of a polynomial in ascending.

8.1 adding and subtracting polynomials Day 1. Monomial “one term” Degree of a monomial: sum of the exponents of its variables. Zero has no degree. a.

CFU Add, subtract, and multiply polynomials including squaring a binomial. SPI Operate with polynomials and simplify results.

Lesson 4.1: Understanding Polynomial Expressions (Pgs )

Polynomials Objectives The student will be able to: 1. find the degree of a polynomial and 2. arrange the terms of a polynomial in ascending or descending.

NO! NO NEGATIVE EXPONENTS ALLOWED. ONLY 0 AND POSITIVES (WHOLE NUMBERS)

Polynomials Monomial---1 term A number, variable or the product of a number and a variable Terms Monomials separated by addition or subtraction signs A.

Terms Monomials separated by addition or subtraction signs Polynomials A monomial or the sum of monomials Binomial---2 terms Trinomial---3 terms Monomial---1.

Objectives 1. find the degree of a polynomial.

Ch 7-4 Polynomials Objectives The student will be able to:

Lesson 4.1 Understanding Polynomial Expressios

POLYNOMIALS REVIEW Classifying Polynomials

Introduction to Polynomials

Polynomials and Factoring

Unit #2 Polynomials.

Intro to Polynomials.

Adding and Subtracting Polynomials

Objectives The student will be able to:

Objectives The student will be able to:

Introduction to Polynomials

A number, a variable or the product of them

Objectives The student will be able to:

1. Find the degree of a polynomial.

descending order of exponents

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

Understanding polynomials

Objectives The student will be able to:

Objectives The student will be able to:

Classifying Polynomials

Introduction to Polynomials

Objectives The student will be able to:

4.1 Introduction to Polynomials

Objectives The student will be able to:

7.3 Polynomials A monomial or a sum of monomials

Classifying Polynomials

Learning Target: I will be able to identify polynomials

CLASSIFYING POLYNOMIAL

Do Now: Aim: How do we work with polynomials?

Presentation transcript:

Classifying Polynomials What you WILL Learn: 1) To find the degree of a polynomial 2) To arrange the terms of a polynomial so that the powers of a variable are in ascending or descending order.

The prefix “mono” means 1 Monomial: one term (no + or -) The prefix “mono” means 1 Can you name a monomial?

Binomial: two terms (separated by + or -) The prefix “bi” means 2 Can you name a binomial?

Trinomial: three terms (separated by + or -) The prefix “tri” means 3 Can you name a trinomial?

The prefix “poly” means many Polynomial: four terms or more (separated by + or -) The prefix “poly” means many Can you name a quadnomial?

The prefix “poly” means MANY Polynomial: a monomial or a sum of monomials. (separated by + or -) Many terms. The prefix “poly” means MANY Can you name a polynomial?

1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial Determine the name of the polynomial. 1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial Trinomial Binomial Trinomial

6) 5) Monomial 4 term polynomial 7) 5 term polynomial Determine the name of the polynomial. 6) 5) 4 term polynomial Monomial 7) 5 term polynomial

DESCENDING: means decreasing. Going from big to small. Descending Order: Exponents go from BIG TO SMALL! *Constants always go last because they have a degree of zero. Example: 3x2 + 7x + 5

Descending order is often referred to as standard form. You should always write your answers in standard form!

2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4 Rewrite the following in descending order. 2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4 3. 7x6 + x2 + 24 – x3 7x6 – x3 + x2 +24

2x4 + 3x Remember: A coefficient is a number in front of a variable.

A leading coefficient is the coefficient of the FIRST TERM when the polynomial is written in descending order (standard form). 2x3 + 4x + 5 Leading coefficient

Leading coefficient = -1 -x5 + x4 + 2x +4; Write the polynomial in descending order (standard form). Then name the leading coefficient. 4. Leading coefficient = 2 2x2 + 3x - 1; 5. Leading coefficient = -1 -x5 + x4 + 2x +4; 6. Leading coefficient = 4 4x3 + x2 + 2x – 7 ;