Warm-up Nov. 15 Lovely quiz day! Remember that you only have 15 minutes. Good luck! HW #5: red text pg. 149 #s 15, 18, & 31 - 51 (1 st column) use pp.

Slides:

Advertisements

Similar presentations

Defining Polynomials Adding Like Terms

Advertisements

(Combining Like Terms)

ZEROS=ROOTS=SOLUTIONS Equals x intercepts. Another Memory slide.

Introduction to Polynomials Adding and Subtracting.

Chapter 6 Polynomials.

Do Now 2/22/10 Copy HW in your planner.Copy HW in your planner. –Text p. 557, #4-28 multiples of 4, #32-35 all In your notebook on a new page define the.

Polynomials Defining Polynomials Adding Like Terms.

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)

Polynomial Functions and Adding and Subtracting Polynomials

Lesson 8-1 Warm-Up.

Combine Like Terms 1) 3x – 6 + 2x – 8 2) 3x – x ) 10xy + 5y – 6xy – 14y 5x – 14 15x + 3 4xy – 9y Warm up.

Adding & Subtracting Polynomials

Unit 2: Algebra Lesson 1 – Introduction to Polynomials Learning Goals: I can simplify polynomial expressions.

Warm Up Simplify each expression: 1.(-4) (5x) 2 5x 1 4.-(-4.9) 0 5.[(3x 4 y 7 z 12 ) 5 (–5x 9 y 3 z 4 ) 2 ] 0.

Degree The largest exponent Standard Form Descending order according to exponents.

Section 9-1 Adding and Subtracting Polynomials SPI 12C: add and subtract algebraic expressions Objectives: Classify a polynomial by degree and number of.

Chapter 9.1 Notes: Add and Subtract Polynomials Goal: You will add and subtract polynomials.

9.1 Adding & Subtracting Polynomials & - Polynomials Goals / “I can…” Describe polynomials Add and subtract polynomials.

4.2 Adding and Subtracting Polynomials Objective: To add and subtract polynomials. Warm – up: Simplify: 1) 6x + 7y + 4x2) m – 6 + 4m 3) -(5a – 2b.

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.

2.3 Factor and Solve Polynomial Expressions Pg. 76.

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:

Polynomials. Polynomial Term Binomial Trinomial 1 or more monomials combined by addition or subtraction each monomial in a polynomial polynomial with.

Adding and subtracting polynomials. Types of polynomials Monomial Binomial Trinomial Polynomial 1 2x 7xy⁵ -12a + b w - m² a² + x⁴ - n³ x + d – 3y + m⁸.

Adding and subtracting polynomials

Essential Question How do you add and subtract polynomials?

Wed, 3/23 SWBAT…add and subtract polynomials Agenda 1. Adding & subtracting polynomials (10 min) 2. Multiplying a monomial by a polynomial (10 min) Warm-Up:

Honors Advanced Algebra Lesson 2-1. Warm-up Simplify the following by combining like terms. 1. 2xyz + 4x + 5y + 2x – 3z – 2y – xyz 2. 3x 2 + 4x 3 – 2x.

December 3, 2012 At the end of today, you will be able to add, subtract and multiply polynomials. Warm-up: 1)Find the x and y intercepts for 2x – 3y =

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 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.

Objective: I will add and subtract polynomials by combining like terms.

Name ____________________________________________ Date _______________ Per_____ Polynomials Review Adding Ex: 1. Simplify 2. Find the perimeter Subtracting.

Adding and subtracting polynomials 1L interpret expressions that represent a quantity in terms of its context.

In this lesson we will classify, add and subtract polynomials.

Bell Ringer Simplify by combining like terms: 1. 2x – 6 + 5x + 9 = y – 7y + 5 = 3. 4x – 6y – 2x + 9y = 7x y + 8 2x + 3y.

5.2 Polynomials Objectives: Add and Subtract Polynomials

Polynomial Functions and Adding and Subtracting Polynomials

8-1 Adding and Subtracting Polynomials

Aim: How do we multiply polynomials?

7.1 – Adding & Subtracting Polynomials

POLYNOMIALS REVIEW Classifying Polynomials

Polynomials By: Ms. Guarnieri.

Adding and Subtracting Polynomials

Introduction to Polynomials

Lesson 5.3 Operations with Polynomials

Adding and Subtracting Polynomials

Defining Polynomials Adding Like Terms

-3x² + 2x + 8 Do Now 2/22/12 Copy HW in your planner.

Defining Polynomials Adding Like Terms

Polynomials A polynomial is a sum of monomials. Common polynomials:

Polynomial Vocabulary and Adding & Subtracting Polynomials

Defining Polynomials Adding Like Terms

Dr. Fowler  CCM Adding Polynomials.

4.1 Introduction to Polynomials

Polynomials and Special Products

Working with monomials and polynomials

3.4 Solve by Factoring (Part 1)

January 10: Opening Quiz 6) 2x - 5 = 1 3x + 6 = 9 7) 2c + 4 = 12

Polynomial Review / Adding, Subtracting, and Multiplying Polynomials

January 10: Opening Quiz 6) 2x - 5 = 1 3x + 6 = 9 7) 2c + 4 = 12

Warm-up: Simplify. Put in standard form.

Adding & Subtracting Polynomials

Do Now 2/1/19 Copy HW in your planner.

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

Presentation transcript:

Warm-up Nov. 15 Lovely quiz day! Remember that you only have 15 minutes. Good luck! HW #5: red text pg. 149 #s 15, 18, & (1 st column) use pp. 9 & 10

Notes #3: Combining Polynomials HW #5: red text pg. 149 #s 15, 18, & (1 st column) use pp. 9 & 10

Monomials - a number, a variable, or a product of a number and one or more variables. 4x, 20x 2 yw 3, -3, a 2 b 3, and 3yz are all monomials. Polynomials – one or more monomials added or subtracted 4x + 6x 2, 20xy - 4, and 3a 2 - 5a + 4 are all polynomials. Vocabulary

Binomial : a polynomial with two terms, such as ex1. 3x + 4 ex2. 5m 2 + 6m Trinomial: a polynomial with three terms, such as ex3. 5c 2 + 4c – 1 ex4. -12xy + 3y + 9 Constant: any term that doesn’t have a variable in it. Like terms: t erms with the same base 1 st term 2nd term constant 1st term 2nd term 3rd term constant

How do you remember the names? Think cycles! There are special names for polynomials with 1, 2 or 3 terms: 3xy 2 Monomial (1 term) 5x – 1 Binomial (2 terms) 3x + 5y 2 – 3 Trinomial (3 terms) bicycle tricycle Monocycle or Unicycle

Like Terms Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers. Which terms are like? 3a 2 b, 4ab 2, 3ab, -5ab 2 4ab 2 and -5ab 2 are like. Even though the others have the same variables, the exponents are not the same. 3a 2 b = 3aab, which is different from 4ab 2 = 4abb.

Add: (x 2 + 3x + 1) + (4x 2 + 5) Add the coefficients of like terms, do not change the powers of the variables: Adding Polynomials 4x Example 1: x 2 + 3x + 1 5x 2 + 3x + 6

Adding Polynomials Ex. 2 Add these polynomials: (2a 2 + 3ab + 4b 2 ) + (7a 2 + ab – 2b 2 ) 2a 2 + 3ab + 4b 2 7a 2 + ab – 2b 2 9a 2 + 4ab + 2b 2

3.) Add: (12a 3 – 12a – 3) + (14a a + 4) 26a 3 + 4a a 3 – 12a – 3 14a a + 4 +

Subtract: (3x 2 + 2x + 7) – (x 2 + x + 4) Subtracting Polynomials When subtracting polynomials, Change the signs of the second polynomial. Remember to place a 1 in front of a variable without a coefficient. 1 st polynomial2 nd polynomial Example 4: 3x 2 + 2x + 7 1x 2 + 1x + 4 2x 2 + x + 3

5.) Subtract: (5x 2 – 4) – (2x 2 + 3) Steps: 1.Line up the like terms together. 2.Change the signs of the second polynomial. 3.Combine like terms Steps: 1.Line up the like terms together. 2.Change the signs of the second polynomial. 3.Combine like terms 1 st polynomial 2 nd polynomial 5x 2 – 4 -2x 2 – 3 3x 2 – 7

6.) Subtract: (-4x 2 – 3x + 6) – (3x 2 + 4x – 3) Change the signs of the 2 nd poly -7x 2 – 7x x 2 – 3x x 2 – 4x + 3

Subtract (3b 2 + 5b + 2) from (8b 2 + 4b – 6). 8b 2 + 4b – 6 -3b 2 – 5b – 2 5b 2 – b – 8 Exit Question