Factoring Using the Distributive Property

Slides:

Advertisements

Similar presentations

5-4 Factoring Quadratic Expressions

Advertisements

Factoring 0-3. Two Ways to Factor Using GCF Using Grouping Using Grouping Through Sums and Factors.

Factoring Trinomials of the form x 2 + bx + c Chapter 5.3.

8-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz

Multiplying Polynomials Be able to use different methods to multiply two polynomials.

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.

Warm-up: Simplify. 1.6 (3x - 5) = 18x (2x + 10) = 8x y - 3y = 6y 4.7a + 4b + 3a - 2b = 10a + 2b 5.4 (3x + 2) + 2 (x + 3) = 14x + 14.

 FACTORING a polynomial means to break it apart into its prime factors.  For example:  x 2 – 4 = (x + 2)(x – 2)  x 2 + 6x + 5 = (x + 1)(x + 5)  3y.

Factoring By Lindsay Hojnowski (2014) Buffalo State College 04/2014L. Hojnowski © Click here to play tutorial introduction Greatest Common Factor.

10.1 Adding and Subtracting Polynomials

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

8.3 Factoring Quadratic Equations Objective The student will be able to: Factor trinomials with grouping. Solve quadratic equations using Zero Product.

9.1 Adding and Subtracting Polynomials

Monomials and Polynomials

Recall: By the distributive property, we have x ( x + 2 ) = x² + 2x Now we’re given a polynomial expression and we want to perform the “opposite” of the.

Multiplying and Factoring Module VII, Lesson 2 Online Algebra

Chapter 8: Factoring.

5.4 Factoring Greatest Common Factor,

Chapter Factoring by GCF.

Factoring Review EQ: How do I factor polynomials?.

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

Factoring by GCF. Factoring Put the expression in a division tower Continue to divide by numbers or variables until there is no number or variable common.

Factoring Quadratic Trinomials. OUTLINE I. Put in descending order of exponents like ax²+bx+c and multiply a*c II. Find two numbers whose product is (a*c),

8.8 Factoring by Grouping. Factoring by grouping USE WHEN THERE ARE 4 TERMS IN THE POLYNOMIAL. Polynomials with four or more terms like 3xy – 21y + 5x.

Algebra 1 O.T.Q. Simplify (–2) 2 4. (x) 2 5. –(5y 2 ) x2x (m 2 ) 2 m4m4 –5y 2.

Objective The student will be able to: factor trinomials of the type ax 2 + bx + c with grouping. Designed by Skip Tyler, Varina High School.

Factoring Trinomials with Common Factors Grouping Method.

Factoring. Objective The student will be able to: Factor trinomials with grouping and Trial & Error. MM1A2f.

SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

Day Problems Simplify each product. 1. 8m(m + 6) 2. -2x(6x3 – x2 + 5x)

Factoring - Difference of Squares What is a Perfect Square.

Factor higher degree polynomials by grouping.

Divide a polynomial by a binomial

Greatest Common Factor and Factoring by Grouping List all possible factors for a given number. 2.Find the greatest common factor of a set of numbers.

8.2B Factoring by Grouping Objectives The student will be able to: use grouping to factor polynomials with four terms use the zero product property to.

8-2 Factoring by GCF Multiplying and Factoring. 8-2 Factoring by GCF Multiplying and Factoring Lesson 9-2 Simplify –2g 2 (3g 3 + 6g – 5). –2g 2 (3g 3.

Objective Factor polynomials by using the greatest common factor.

Factoring Polynomials

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

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.

9-2 Factoring Using the Distributive Property Objectives: 1)Students will be able to factor polynomials using the distributive property 2)Solve quadratic.

Math 9 Lesson #34 – Factors and GCF/Factoring with Distributive Property Mrs. Goodman.

Objective The student will be able to: multiply two polynomials using the distributive property.

I can factor trinomials with grouping.. Factoring Chart This chart will help you to determine which method of factoring to use. TypeNumber of Terms 1.

Warm Up 1) 2(w + 1) 2) 3x(x 2 – 4) 2w + 23x 3 – 12x 2h Simplify. 13p Find the GCF of each pair of monomials. 3) 4h 2 and 6h 4) 13p and 26p 5.

Factoring by Grouping Section 8-8. Goals Goal To factor higher degree polynomials by grouping. Rubric Level 1 – Know the goals. Level 2 – Fully understand.

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.

Factoring Polynomials Factoring is the process of changing a polynomial with TERMS (things that are added or subtracted) into a polynomial with THINGS.

Factoring Trinomials SWBAT: Factor Trinomials by Grouping.

Lesson 9-2 Factoring Using the Distributive Property.

Using the Distributive Property, Factoring by Grouping (8-2)

8-2 Multiplying Polynomials

Factoring Polynomials

Objective Factor polynomials by using the greatest common factor.

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

7-5 Multiply a Polynomial by a Monomial

Algebra 1 Section 10.1.

Objectives The student will be able to:

Factoring Using the Distributive Property

Before: February 5, 2018 Factor each polynomial. Check your answer.

ZERO AND NEGATIVE EXPONENT Unit 8 Lesson 8

Factoring by GCF CA 11.0.

Grade Distribution 2/17/2019 7:48 PM Common Factors.

7-2 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz

Factoring Polynomials

Objective Factor polynomials by using the greatest common factor.

Factoring Polynomials.

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

Objective Factor polynomials by using the greatest common factor.

Presentation transcript:

Factoring Using the Distributive Property GCF and Factor by Grouping

Review 1) Factor GCF of 12a2 + 16a 12a2 = 16a = Use distributive property

Using GCF and Grouping to Factor a Polynomial First, use parentheses to group terms with common factors. Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

Using GCF and Grouping to Factor a Polynomial First, use parentheses to group terms with common factors. Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

Using GCF and Grouping to Factor a Polynomial First, use parentheses to group terms with common factors. Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

Using the Additive Inverse Property to Factor Polynomials. When factor by grouping, it is often helpful to be able to recognize binomials that are additive inverses. 7 – y is y – 7 By rewriting 7 – y as -1(y – 7) 8 – x is x – 8 By rewriting 8 – x as -1(x – 8)

Factor using the Additive Inverse Property. Notice the Additive Inverses Now we have the same thing in both ( ), so put your answer together.

Factor using the Additive Inverse Property. Notice the Additive Inverses Now we have the same thing in both ( ), so put your answer together.

There needs to be a + here so change the minus to a +(-15x) Now group your common terms. Factor out each sets GCF. Since the first term is negative, factor out a negative number. Now, fix your double sign and put your answer together.

There needs to be a + here so change the minus to a +(-12a) Now group your common terms. Factor out each sets GCF. Since the first term is negative, factor out a negative number. Now, fix your double sign and put your answer together.

Summary A polynomial can be factored by grouping if ALL of the following situations exist. There are four or more terms. Terms with common factors can be grouped together. The two common binomial factors are identical or are additive inverses of each other.