Chapter 5 Polynomials.

Slides:



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

Polynomials Identify Monomials and their Degree
Dividing Polynomials Monomials (Ex: 2x): It divides into everything…
5.3 – Polynomials and Polynomial Functions Definitions Coefficient: the numerical factor of each term. Constant: the term without a variable. Term: a number.
Intermediate Algebra A review of concepts and computational skills Chapters 4-5.
Exponents and Polynomials
Section 5.1 Polynomials Addition And Subtraction.
Section R3: Polynomials
Multiplying and Dividing Polynomials Chapter 5 Sections
Drill #17 Simplify each expression.. Drill #18 Simplify each expression.
Monomials – Product and Quotient Remember your rules for multiplying and dividing variables…- When multiplying like variables, ADD your exponents When.
1 linearf (x) = mx + bone f (x) = ax 2 + bx + c, a  0quadratictwo cubicthreef (x) = ax 3 + bx 2 + cx + d, a  0 Degree Function Equation Common polynomial.
Section 4.1 The Product, Quotient, and Power Rules for Exponents.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.
3.7Divide Polynomials Example 1 Divide a polynomial by a monomial Divide 10x 3  25x x by 5x. Solution Method 1: Write the division as a fraction.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.
Chapter 6 – Polynomials and Polynomial Functions
1.2 - Products Commutative Properties Addition: Multiplication:
 We use the acronym below to multiply two binomials. F – O – I – L – FIRST OUTSIDE INSIDE LAST.
6.3 Adding, Subtracting, & Multiplying Polynomials p. 338.
Degree The largest exponent Standard Form Descending order according to exponents.
MATHPOWER TM 10, WESTERN EDITION Chapter 3 Polynomials
How do you perform operations with polynomials? Section P4 (old text)
Multiplication: Special Cases Chapter 4.5. Sum x Difference = Difference of Two Squares (a + b)(a – b) = (a – b)(a + b) =a 2 – b 2.
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!”
Chapter 5 Polynomials: An Introduction to Algebra.
Warm-up: 9/9 Factor the following polynomials a.) b.) c.)
Dividing Polynomials – Part 2 Honors Math – Grade 8.
Dividing Polynomials SYNTHETIC DIVISION AND LONG DIVISION METHODS.
5.3 Dividing Polynomials Objectives: 1.Divide polynomials using long division 2.Divide polynomials using synthetic division.
10.6 – Special Products of Polynomials Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms.
6.1 Review of the Rules for Exponents
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.
Copy down the following expressions and circle the like terms. 1. 7x 2 + 8x -2y + 8 – 6x 2. 3x – 2y + 4x 2 – y 3. 6y + y 2 – 3 + 2y 2 – 4y 3 What are like.
Polynomials Objective: To review operations involving polynomials.
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.
8.1 ADDING AND SUBTRACTING POLYNOMIALS To classify, add, and subtract polynomials.
Dividing Polynomials/Long and Synthetic Division Section 6.3.
Algebra 2a September 13, 2007 Chapter Five review.
Name ____________________________________________ Date _______________ Per_____ Polynomials Review Adding Ex: 1. Simplify 2. Find the perimeter Subtracting.
CHAPTER 12 Polynomials: Operations Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 12.1Integers as Exponents 12.2Exponents and Scientific.
5.3 Notes – Add, Subtract, & Multiply Polynomials.
Adding and Subtracting Polynomials
AIM: How do we multiply and divide polynomials?
Polynomials and Polynomial Functions
Polynomials and Polynomial Functions
Dividing Polynomials Section 4.3.
Polynomials and Polynomial Functions
TEST.
8-1 Adding and Subtracting Polynomials
Multiplying and Dividing Polynomials
7.8 Multiplying Polynomials
Mohandas Karamchand Gandhi
Section 6.3 Dividing Polynomials
Exponents, Polynomials, and Polynomial Functions
Add, Subtract and Multiply Polynomials
Polynomials and Polynomial Functions
5 Section 5 Dividing Polynomials.
Exponents and Polynomials
Multiplying and Dividing Polynomials
Section P4 Polynomials.
4.1 Introduction to Polynomials
Section 5.6 Dividing Polynomials.
Lesson 7.4 Dividing Polynomials.
Working with monomials and polynomials
Synthetic Division The shortcut.
3.7 Divide Polynomials - + Divide a polynomial by a monomial = =
Exponents, Radicals, Polynomials…
Synthetic Division Notes
Presentation transcript:

Chapter 5 Polynomials

Sect. 6.1 Using the Rules of Exponents

Examples of Using Rules of Exponents cont

Sect. 6.2 Addition and Subtraction of Polynomials

Examples of Polynomials d.) Is a pollynomial. The degree is 5, which is the degree of the term also.

Evaluate Polynomials Ex. 2

Add Polynomials in One Variable Ex. 3 Ex. 4

Subtract Polynomials in One Variable Ex. 5

Subtracting Horizontally and Vertically Ex. 6

Add and Subtract Polynomials in More than One Variable Ex. 7

Define and Evaluate a Polynomial Function Ex. 8

Sect. 6.3 Multiplication of Polynomials

Multiply Two Polynomials Ex. 1

Multiply Two Polynomials Vertically Ex. 3

Multiply Two Binomials Using FOIL Ex. 4 Use FOIL to multiply (y + 4)(y + 7)

Multiply Two Binomials Using FOIL cont. Ex. 5 Multiply (3a - 2b)(a + b)

Find the Product of More than Two Polynomials Ex. 6

Find the Product of Binomials of the Form (a + b)(a - b) Ex. 7

Square a Binomial

Example of Squaring a Binomial

Find Higher Powers of a Binomial Ex. 9

Sect. 6.4 Division of Polynomials Ex. 1

Divide Polynomial by Monomial continued

Divide Polynomial by Monomial continued Ex. 2

Divide a Polynomial by a Polynomial 4593/8 = 574 1/8

Divide a Polynomial by a Polynomial cont. So

Divide a Polynomial by a Polynomial cont This is a division problem with a remainder.

Divide a Polynomial by a Polynomial cont

Divide Polynomials with Missing Terms Ex. 6

Divide a Polynomial by a Polynomial Using Synthetic Division Ex. 7

Divide a Polynomial by a Polynomial Using Synthetic Division cont.