Multiplying Polynomials January 29, 2009. Page 416-417 #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial.

Slides:

Advertisements

Similar presentations

5.2 Multiplying Polynomials. To Multiply Polynomials Each term of one polynomial must be multiply each term of the other polynomial.

Advertisements

Chapter 5 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

4.5 Multiplying Polynomials

Multiplication of Polynomials.  Use the Distributive Property when indicated.  Remember: when multiplying 2 powers that have like bases, we ADD their.

Section 9-3 Multiplying Binomials SPI 12D: multiply two polynomials with each factor having no more than two terms Objectives: Multiply binomials by modeling.

§ 4.5 Multiplication of Polynomials. Angel, Elementary Algebra, 7ed 2 Multiplying Polynomials To multiply a monomial by a monomial, multiply their coefficients.

Exponents and Polynomials

Polynomial Expressions Section P.3. Definition of Polynomial An algebraic expression of the form Where all coefficients a i are real numbers, The degree.

Adding and Subtracting Polynomials Section 0.3. Polynomial A polynomial in x is an algebraic expression of the form: The degree of the polynomial is n.

EXAMPLE 1 Multiply a monomial and a polynomial Find the product 2x 3 (x 3 + 3x 2 – 2x + 5). 2x 3 (x 3 + 3x 2 – 2x + 5) Write product. = 2x 3 (x 3 ) + 2x.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

MULTIPLICATION OF POLYNOMIALS CHAPTER 4 SECTION 5 MTH Algebra.

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

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

Chapter 5 Section 5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson.

Multiplying Polynomials; Special Products Multiply a polynomial by a monomial. 2.Multiply binomials. 3. Multiply polynomials. 4.Determine the product.

Multiplying Polynomials

Multiplication of Polynomials

Review Operations with Polynomials December 9, 2010.

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

Aim: How do we multiply polynomials? Do Now: Multiply the following 1. 2x(3x + 1) 2. (x – 1)(x + 2) 3. (x +2)(x 2 – 3x + 1)

POLYNOMIALS – Monomial Times a Polynomial When multiplying a monomial and a polynomial, multiply the monomial by EACH term in the polynomial. It’s called.

Objective - To multiply polynomials. Multiply the polynomial by the monomial. 1) 3(x + 4) 2) 3) Distributive Property.

Multiplying Polynomials January 29, Page #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial.

2.2 Warm Up Find the sum or difference. 1. (2x – 3 + 8x²) + (5x + 3 – 8x²) 2. (x³ - 5x² - 4x) – (4x³ - 3x² + 2x – 8) 3. (x – 4) – (5x³ - 2x² + 3x – 11)

Copyright © 2010 Pearson Education, Inc. All rights reserved. 5.3 – Slide 1.

Multiplying Polynomials. Distributive Method Multiply each term in the first polynomial, by each term in the second polynomial. Combine like terms Example:

Copyright © 2014, 2010, 2006 Pearson Education, Inc. Section 5.3 Slide 1 Exponents and Polynomials 5.

Multiply two binomials using FOIL method

Algebra Multiplying Polynomials. Learning Targets Language Goal Students should be able to read, write, say, and classify polynomials. Math Goal.

The third method is the Box Method. This method works for every problem! Here’s how you do it. Multiply (3x – 5)(5x + 2) Draw a box. Write a polynomial.

Polynomial Functions Addition, Subtraction, and Multiplication.

6.1 Review of the Rules for Exponents

EXAMPLE 3 Multiply polynomials vertically

Polynomials Lesson 5.2: Adding, Subtracting, and Multiplying Polynomials By: Just Just Leininger Period 3 modern algebra.

Multiplying Polynomials with FOIL Objective: Students will multiply two binomials using the FOIL method. S. Calahan March 2008.

Polynomials Objective: To review operations involving polynomials.

Algebra 2a September 13, 2007 Chapter Five review.

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

EXAMPLE 3 Multiply polynomials vertically Find the product (b 2 + 6b – 7)(3b – 4). SOLUTION STEP 1 Multiply by – 4. b 2 + 6b – 7 – 4b 2 – 24b b –

Mrs. Reynolds 2/19/14. When multiplying two binomials, you can use the FOIL Method. FOIL is a series of four steps using the Distributive Property.

Lesson 10.2 Multiplying Polynomials Objective: To multiply polynomials Multiply monomials by other polynomials by using distributive property Examples.

Notes Over 6.3 Adding Polynomial Horizontally and Vertically Find the sum. Just combine like terms.

Multiply two binomials using FOIL method

POLYNOMIALS – Monomial Times a Polynomial

In this lesson, we will multiply polynomials

Multiplying Binomials

AIM: How do we multiply and divide polynomials?

Polynomials and Polynomial Functions

Addition, Subtraction, and Multiplication of Polynomials

Objective - To multiply polynomials.

Adding and Subtracting Polynomials

Multiplication of monomial and binomials.

Polynomials and Polynomial Functions

5.2 Polynomials Objectives: Add and Subtract Polynomials

5.4 Multiplying Polynomials.

Multiplying Polynomials

5-9 Multiplying Monomials and Binomials

Exponents, Polynomials, and Polynomial Functions

Add, Subtract and Multiply Polynomials

13 Exponents and Polynomials.

Multiply polynomials When multiplying powers with the same base, keep the base and add the exponents. x2  x3 = x2+3 = x5 Example 1: Multiplying Monomials.

Warm-Up Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)

Objective multiply two polynomials using the FOIL method and the distributive property.

Warm up: Match: Constant Linear Quadratic Cubic x3 – 2x 7

8-3 Multiplying Polynomials by Using FOIL

(2)(4) + (2)(5) + (3)(4) + (3)(5) =

Objective The student will be able to:

Ch Part 1 Multiplying Polynomials

Multiplying Polynomials

Presentation transcript:

Multiplying Polynomials January 29, 2009

Page #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial 18) Not a polynomial 20) Not classified (quadnomial) 22) binomial 24) 3x 3 + 5x 2 +4, degree is 3 26) x 2 –x+4, degree is 2 28) x 17 -3x 4, degree is 17 30) 15, 0 32) 5, ) 34, 34 36) -1, 19 38) 0, 0

Objectives Find the product of a monomial and a polynomial. Find the product of two polynomials. Square a polynomial. Find the product of two binomials that differ on in sign.

Multiplying a polynomial by a monomial Use the distributive property to multiply each term in the polynomial by the monomial. x(2x+1) 2x 2 +2x

Multiplying polynomials Method 1: The Distributive Property 1.Distribute the first binomial over the second binomial. 2.Multiply. 3.Combine like terms. (2x+1)(x-5) = 2x(x-5)+1(x-5) = 2x 2 -10x+x-5 = 2x 2 -9x+5

Multiplying polynomials Method 2: FOIL (only works for binomials) 1.Multiply the FIRST term of each binomial. 2.Multiply the OUTER term of each binomial. 3.Multiply the INNER term of each binomial. 4.Multiply the LAST term of each binomial. 5.Combine like terms. (3x-1)(2x+2) F O I L 6x 2 +6x -2x -2 = 6x 2 +4x-2

Multiplying Polynomials Method 3: Completing the square. 1.Write each binomial along the sides of a square… 2.Multiply each item… 3.Add the items together… 4.Combine like terms. (3x+4)(2x+1) 6x 2 +8x+3x+4 6x 2 +11x+4 6x 2 8x 3x4

Multiplying polynomials Method 4: Vertical Method 1.Line up the polynomials. 2.Multiply each term, like compound multiplication. 3.Add. 4.Combine like terms. x 2 +3x +5 x x 2 -6x -10 x 3 +3x 2 +5x. x 3 +x 2 -x -10

Squaring a polynomial While you can use the methods for multiplying polynomials, there is a shortcut! 1.Square the first term. 2.Multiply the product of the two terms by two. 3.Square the last term. For example: (x+5) 2 x 2 +(x*5*2)+25 x 2 +10x+25

The product of two binomials that differ only in sign Again, you can use the methods of multiplying polynomials… but why waste time! 1.Square the first term 2.Subtract the square of the second term from the answer in 1. Example: (3x-9)(3x+9) 9x 2 -81

4.5, pages #2-76 even