8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper GMF is similar to GCF. Greatest Monomial Factor is similar.

Slides:

Advertisements

Similar presentations

Extracting Factors from Polynomials

Advertisements

§ 5.4 Factoring Trinomials.

11-2 Rational Expressions

§ 5.4 Factoring Trinomials. Blitzer, Intermediate Algebra, 4e – Slide #42 Factoring Trinomials A Strategy for Factoring T 1) Enter x as the first term.

Introduction to Factoring 2 ∙ 3 = 6 4 ∙ 2 = 8 3 ∙ 3 ∙ 3 ∙ 3 = ∙ 3 ∙ 5 =

Do Now: Write the standard form of an equation of a line passing through (-4,3) with a slope of -2. Write the equation in standard form with integer coefficients.

Multiplying a binomial by a monomial uses the Distribute property Distribute the 5.

© 2007 by S - Squared, Inc. All Rights Reserved.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.1 – Slide 1.

5.1 The Greatest Common Factor; Factoring by Grouping

The Greatest Common Factor and Factoring by Grouping

Introduction to Factoring 2 ∙ 3 = 6 4 ∙ 2 = 8 3 ∙ 3 ∙ 3 ∙ 3 = ∙ 3 ∙ 5 =

Warm Up 1. 2(w + 1) 2. 3x(x2 – 4) 2w + 2 3x3 – 12x 3. 4h2 and 6h 2h

1 Section 1.8 Multiplication of Algebraic Expressions.

The Greatest Common Factor; Factoring by Grouping

Factoring a Monomial from a Polynomial Chapter 5 Section 1

Chapter 9 Polynomials and Factoring A monomial is an expression that contains numbers and/or variables joined by multiplication (no addition or subtraction.

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

Monomials and Polynomials

Monomials Multiplying Monomials and Raising Monomials to Powers.

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

11-8 Mixed Expressions and Complex Fractions Algebra 1 Glencoe McGraw-HillLinda Stamper.

Factoring Polynomials 10-2 (page 565 – 571) Distributing and Grouping

Day 3: Daily Warm-up. Find the product and combine like terms. Simplify each expression (combine like terms)

Chapter 6 Factoring Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1.

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

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Greatest Common Factors; Factoring by Grouping.

REVIEW OF FACTORING Chapters 5.1 – 5.6. Factors Factors are numbers or variables that are multiplied in a multiplication problem. Factor an expression.

Factor Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper.

Warm Up. y = 8x 2 – 16x -10 = roots a = 8, b = – 16, c = -10 Axis of symmetry = -b 2a x = -(-16) 2(8) = 1 y = 8(1) 2 – 16(1) -10 = -18 Vertex= minimum.

Factor Perfect Squares and Factoring Algebra 1 Glencoe McGraw-HillLinda Stamper.

Factoring Polynomials

Objective Factor polynomials by using the greatest common factor.

8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper.

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.

5-4 Factoring Polynomials Objectives: Students will be able to: 1)Factor polynomials 2)Simplify polynomial quotients by factoring.

To factor means to write a number or expression as a product of primes. In other words, to write a number or expression as things being multiplied together.

POLYNOMIALS.  A polynomial is a term or the sum or difference of two or more terms.  A polynomial has no variables in the denominator.  The “degree.

Factors are numbers you can multiply together to get another number Example: 2 and 3 are factors of 6, because 2 × 3 = 6 Objectives: SWBAT 1) find the.

Copyright © 2016, 2012, 2008 Pearson Education, Inc. 1 Factoring out the Greatest Common Factor.

Topic VII: Polynomial Functions Polynomial Operations.

Warm Up Simplify the expression.. 7-2B Division Properties of Exponents RESTRICTION: Note: It is the variable that is restricted – not the exponent! Algebra.

Holt McDougal Algebra Factoring by GCF Warm Up 1. 2(w + 1) 2. 3x(x 2 – 4) 2w + 2 3x 3 – 12x 2h2h Simplify. 13p Find the GCF of each pair of monomials.

MTH 091 Sections 3.1 and 9.2 Simplifying Algebraic Expressions.

Factoring Quadratic Expressions Lesson 4-4 Part 1

9.1 Factors & Greatest Common Factor Methods Examples Practice Problems.

Math 8H Algebra 1 Glencoe McGraw-Hill JoAnn Evans 8-2 Factoring Using the Distributive Property.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec Greatest Common Factors; Factoring by Grouping.

Objective - To multiply polynomials.

Copyright © 2013, 2009, 2006 Pearson Education, Inc.

1-5 B Factoring Using the Distributive Property

Multiplication of monomial and binomials.

§ 5.4 Factoring Trinomials.

Lesson 6.1 Factoring by Greatest Common Factor

8-2 Multiplying Polynomials

11-2 Rational Expressions

Warm Up 1. 50, , 7 3. List the factors of 28. no yes

Objective Factor polynomials by using the greatest common factor.

In the previous section we were multiplying a monomial by a polynomial expression like this… 3

Factoring Polynomials 3

14 Factoring and Applications.

Factoring Using the Distributive Property

6.1 & 6.2 Greatest Common Factor and Factoring by Grouping

Algebra 1 Section 10.3.

Factoring Using the Distributive Property

Section 5.5 Factoring Polynomials

Day 136 – Common Factors.

Unit 1 Section 3B: MULTIPLYING POLYNOMIALS

Objective Factor polynomials by using the greatest common factor.

Using the distributive property to factor polynomials having four or more terms is called factoring by grouping because pairs of terms are grouped together.

Presentation transcript:

8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper GMF is similar to GCF. Greatest Monomial Factor is similar to the Greatest Common Factor.

You have used the distributive property to determine a product – for example: You can also use the distributive property to take the product and return it to factored form – for example: Today you will use the distributive property to factor out constants and or variables that are common terms of a polynomial. A polynomial is prime if it cannot be factored using integer coefficients. To factor a polynomial completely, write it as the product of a monomial and prime factors.

Find the greatest monomial factor. Then factor it out of the expression. Write as prime factors. Circle common primes Find the GMF (multiply the common primes). Use the distributive property to factor out the GMF Check – Multiply the factors together using the distributive property. Whatever is NOT circled goes in parentheses.

Find the greatest monomial factor. Then factor it out of the expression. The problem. Think of the GMF. Use the distributive property to factor out the GMF You are using division when you factor the GMF out of the expression!

Find the greatest monomial factor. Then factor it out of the expression. Write as prime factors. Circle common primes Find the GMF (multiply the common primes). Use the distributive property to factor out the GMF Check – Multiply the factors together using the distributive property. Whatever is NOT circled goes in parentheses.

Find the greatest monomial factor. Then factor it out of the expression. The problem. Think of the GMF. Use the distributive property to factor out the GMF

15x 2 – 20x + 35 What factor do each of these terms have in common? 5 is the GMF. Divide each term by the GMF Rewrite the expression with the GMF outside the parentheses and the resulting divisions inside. 5 (3x 2 - 4x + 7)

Find the greatest monomial factor. Then factor it out of the expression. Write as prime factors. Circle common primes prime

Find the greatest monomial factor. Then factor it out of the expression. Check – Multiply the factors together using the distributive property. Example 1 Example 2

Example 1 Find the greatest monomial factor. Then factor it out of the expression. Check – Multiply the factors together using the distributive property. ( )

Example 2 Find the greatest monomial factor. Then factor it out of the expression. Check – Multiply the factors together using the distributive property. ( )

Example 3 Find the greatest monomial factor. Then factor it out of the expression. Example 4 Example 5 Example 6

Using the distributive property to factor polynomials having four or more terms is called factoring by grouping because pairs of terms are grouped together and factored. The distributive property is then applied a second time to factor a common binomial factor. Group terms with common factors. Factor the GMF from each group. Factor the common binomial factor. Check – Multiply the factors together using FOIL. The problem.

Sometimes you can group terms in more than one way when factoring a polynomial. Here is an alternate way to group the previous problem. Group terms with common factors. Factor the GMF from each group. Factor the common binomial factor. Notice that this result is as the previous grouping. The problem.

Be careful when factoring out a negative value! Group terms with common factors. Factor the GMF from each group. Factor the common binomial factor. The problem. Undo double sign!

Factor the polynomial. Check – Multiply the factors together using FOIL. Example 9 Example 10 Example 7 Example 8

Factor the polynomial. Check – Multiply the factors together using FOIL. Example 7 Example 8

Factor the polynomial. Check – Multiply the factors together using FOIL. Example 9 Example 10 Undo double sign!

8-A3 Page 423 # 19–27,29 and Pages # 9–20,45.