Factoring GCF and Trinomials.

Slides:

Advertisements

Similar presentations

Objectives The student will be able to: 1. find the prime factorization of a number. 2. find the greatest common factor (GCF) for a set of monomials.

Advertisements

Section 5.1 Prime Factorization and Greatest Common Factor.

GCF & LCM - Monomials.

2.2 – Factoring Polynomials Common Factoring. Whenever we are asked to factor the first thing that we should do is look for common factors. The Greatest.

Greatest Common Factor (GCF) and Least Common Multiple (LCM)

9.1 Factors and Greatest Common Factors What you’ll learn: 1.To find prime factorizations of integers and monomials. 2.To find the greatest common factors.

GREATEST COMMON FACTOR

Greatest Common Factor

EXAMPLE 4 Finding the GCF of Monomials

GREATEST COMMON FACTOR

Objectives The student will be able to: 7A: Find the prime factorization of a number, the greatest common factor (GCF) for a set of monomials and polynomials.

Chapters 8 and 9 Greatest Common Factors & Factoring by Grouping

11.1 – The Greatest Common Factor (GCF)

Do Now Find the GCF of each set of numbers. 1)34, 51 2)36, 72 3)21, 42, 56.

Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, , 55 GCF = 3 GCF.

FACTORING. Factoring a Monomial From a Trinomial.

CHAPTER 8: FACTORING FACTOR (noun) –Any of two or more quantities which form a product when multiplied together. 12 can be rewritten as 3*4, where 3 and.

GCF What does it stand for? What is it?. What do these have in common??

Factoring Polynomials: Part 1

Objectives The student will be able to: Factor using the greatest common factor (GCF). SOL: A.2c Designed by Skip Tyler, Varina High School.

Simple Factoring Objective: Find the greatest common factor in and factor polynomials.

Greatest Common Factor Lesson 3-3. Greatest Common Factor (GCF) The greatest common factor is the largest factor that two numbers share. Let’s find the.

Factoring Polynomials: Part 1 GREATEST COMMON FACTOR (GCF) is the product of all prime factors that are shared by all terms and the smallest exponent of.

REMEMBER: What is a factor? What are the factors of 24?

Sec. 9-2: Multiplying & Factoring. To multiply a MONOMIAL with a polynomial, simply distribute the monomial through to EACH term of the polynomial. i.e.

GCF Factoring To find the GCF between two or more terms: 1)Factor Tree 2)List all factors 3)Find the largest # and variable that goes into all terms.

Keep in Your Notes!! list the first 15 perfect squares 1² = 2² = 3² =

Factors When two numbers are multiplied, each number is called a factor of the product. List the factors of 18: 18:1, 2, 3, 6, 9, 18 * Calculators: Y =

Adding and Subtracting Polynomials Multiplying Polynomials Factoring Polynomials.

Topic #3: GCF and LCM What is the difference between a factor and a multiple? List all of the factors and the first 3 multiples of 6.

Factoring Polynomials. Part 1 The Greatest Common Factor.

Topic: Factoring MI: Finding GCF (Greatest Common Factor)

Objectives The student will be able to:

Greatest Common Factor

8.2A Factoring using Distributive Property

Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

Warm-Up Section8.1 (Add to Separate Piece of Paper)

Objectives The student will be able to:

Factoring Trinomials.

(12x2 + 8x – 6) – (9x2 – 2x + 5) Find the area (x – 5)(-3x2 + 6x – 8)

Simplest Type of Factoring

Factor. x2 – 10x x2 – 16x + 1 Multiply. 3. (4x- 3y)(3x +4y)

Factoring trinomials ax² + bx +c a = 1

Objectives The student will be able to:

Factoring Polynomials

= x2 + 8x + 12 = x2 – 81 = x2 – 6x + 9 = 2x2 + 5x – 25 = x2 – 16

Answers to Unit 1, Lesson 1 Exercises

Greatest Common Factor

Objectives The student will be able to:

Objectives The student will be able to:

Bell Ringer 10/27/10 What is the GCF? 18x³y² and 24x² ab and a³b².

Warm Up Rewrite -6x + 2x3 + 1 – 9x in standard form, then name by degree & number of terms. 2) Multiply (x + 3)(5x – 1) 3) Multiply (x – 1)(4x2 +5x –

Warm Up 1. Which of the following is an example of the Associative Property? A = B = 9 C. 9( ) = 9(10) + (11) D.

Factoring Polynomials.

Objectives The student will be able to:

The Greatest Common Factor and Factoring by Grouping

Factoring Polynomials.

Greatest Common Factors & Factoring by Grouping

Objective Factor polynomials by using the greatest common factor.

Objectives The student will be able to:

Objective Factor polynomials by using the greatest common factor.

Objectives The student will be able to:

Factoring using the greatest common factor (GCF).

Objectives The student will be able to:

Objectives The student will be able to:

Factoring Polynomials

Objectives The student will be able to:

ALGEBRA I - SECTION 8-2 (Multiplying and Factoring)

Greatest Common Factor

Presentation transcript:

Factoring GCF and Trinomials

Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 6, 9 15, 55 GCF = 3 GCF = 5

3. What is the greatest common factor?? 36 24 The number 12

GCF with Variables Note: With variables, the GCF will Always be the smallest exponent of a Common variable Examples: 12x3, 16x2 45a5, 50a7 GCF = 4x2 GCF = 5a5

6. What is the greatest common factor?? The GCF is 5a

What is the greatest common factor?? 7. 3y -8xy y 11x 8. 22x2 – 11x -x2 9. -4x6 - x4 - 2x2

Factoring means to write as a product Always look for a Greatest Common Factor 1st. Factor 4x + 6y What is their greatest common factor? = 2( ) 2x + 3y Lets check. =2(2x+3y) = 4x+6y

= y( ) 3 – 8x = 2a( ) a2 – 3b2 Factor 11. 3y – 8xy 12. 2a3 – 6ab2 What is their GCF? = y( ) 3 – 8x 12. 2a3 – 6ab2 = 2a( ) a2 – 3b2

= 2k( ) h2 + 1 = 3v( ) 2u + 3v Factor 13. 2h2k + 2k 14. 6uv + 9v2 What is their GCF? = 2k( ) h2 + 1 14. 6uv + 9v2 = 3v( ) 2u + 3v

What if there is not GCF? 3x + 2 Then it is prime x2 + 3x + 2 Unless it is a trinomial, then I have to use another method.

GCF Factor: xy – 5y What is common? Answer: y(x - 5) What if we change the expression slightly? x(x + 4) – 5(x + 4) Answer: (x + 4)(x – 5 )

GCF Try these: 3x2 – 6x – 15x3 16x2 – 8x y(y – 6) + 9(y – 6)