Greatest Common Factor

Slides:

Advertisements

Similar presentations

Factoring Polynomials.

Advertisements

Extracting Factors from Polynomials

GCF & LCM - Monomials.

Polynomials 02/11/12lntaylor ©. Table of Contents Learning Objectives Adding Polynomials Distributing Negative Signs Multiplying Polynomials Special Case.

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

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

MTH 091 Section 11.1 The Greatest Common Factor; Factor By Grouping.

Unit 9 – Factoring Polynomials

The Greatest Common Factor and Factoring by Grouping

Day 1 – Polynomials Multiplying Mrs. Parziale

Intermediate Algebra A review of concepts and computational skills Chapters 4-5.

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.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 6.1 Removing a Common Factor.

Polynomials and Factoring Review By: Ms. Williams.

11.1 – The Greatest Common Factor (GCF)

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.

Find the GCF of each pair of monomials: 1.3x 2, 9x 3 2.p 2 q 3, p 3 q ab 2, 48bc Factor: 4.10b + 25b x 3 y 5 + 7x 2 y 6.4a + 8b + 12 Solve.

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.

Chapter 10 Section 3 Identifying Polynomials Greatest Common Factor.

PATTERNS, ALGEBRA, AND FUNCTIONS

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

Adding & Subtracting Polynomials

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

Factoring. With quadratics, we can both expand a binomial product like (x + 2)(x + 5), or similar, and go the other way around Factoring = taking.

Polynomials By C. D.Toliver. Polynomials An algebraic expression with one or more terms –Monomials have one term, 3x –Binomials have two terms, 3x + 4.

6-1 Polynomial Functions Classifying polynomials.

13.01 Polynomials and Their Degree. A polynomial is the sum or difference of monomials. x + 3 Examples: Remember, a monomial is a number, a variable,

Lesson 2.1 Adding and Subtracting Polynomials..

Bellwork Simplify the following by combining like terms.

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.

Understanding Polynomials

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 6.4, Slide 1 Chapter 6 Polynomial Functions.

Chapter 5 Section 4 Factoring Quadratic Expressions.

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. 5x 3 + 2x 2 – x – 7 5x 3 + 2x 2 – x – 7 This is a polynomial in standard form: Leading Coefficient Degree Constant.

Factoring a polynomial means expressing it as a product of other polynomials.

DO NOW 11/12/14 Homework in the basket please Multiply the following polynomials 1. (3x + 1)(3x – 1) 1. (2z – 7)(z + 4) 1. (4a + 2)(6a2 – a + 2) 1. (7r.

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.

Polynomials and Polynomial Functions

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

Warm-up Find the GCF for the following: 36, 63, 27 6x2, 24x

Polynomial Operations

Factors & Greatest Common Factors

Lesson 10.4B : Factoring out GCMF

Review Lesson Monomials.

Aim: How do we multiply polynomials?

Introduction to Polynomials

Dividing Polynomials.

Lesson 7-4 Polynomials p. 424.

Lesson 5.3 Operations with Polynomials

Class Greeting.

Polynomials Monomials & Operations

Factoring GCF and Trinomials.

Naming Polynomials Add and Subtract Polynomials Multiply Polynomials

Factoring Polynomials.

Keeper 1 Honors Calculus

A number, a variable or the product of them

3.5 Many of the topics in 3.5 will be a review of concepts worked on in gr. 9. Lets see what you remember.

6.1 & 6.2 Greatest Common Factor and Factoring by Grouping

Homework Review.

Dividing Polynomials.

Factoring Polynomials.

Objective Factor polynomials by using the greatest common factor.

Objective Factor polynomials by using the greatest common factor.

Polynomial Vocabulary

Warm-up Find the GCF for the following: 36, 63, 27 6x2, 24x

CLASSIFYING POLYNOMIAL

Presentation transcript:

Greatest Common Factor Chapter 6 Lesson 1 Greatest Common Factor

Greatest Common Factor What do you think this means?

Often abbreviated as: GCF Definition Greatest Common Factor: the largest monomial that divides (is a factor of) each term of the polynomial. Often abbreviated as: GCF

Let’s compare! Left: Best friend, Wes. Right: Your teacher, Mr. Stillwell. Looking at these two pictures, what do Wes and Mr. Stillwell have in COMMON? Red Helmets Caucasian Glasses Outside Male

Greatest Common Factor! We compared the two pictures…. Greatest Common Factor is the same! Find everything each term (of a polynomial) have in common!

Find GCF (greatest common factor) To find the GCF, there are 5 steps to follow: What do we know about the polynomial? How many terms? Monomial, Binomial or Trinomial?

2. What must we find? Largest number that divides into each coefficient (Factor tree) Largest variable that divides into each coefficient (smallest exponent)

3. Calculate the GCF by multiplying the constant and variable you found in step #2.

4. Rewrite our polynomial with the GCF.

5. Check our answer!

Step by Step… Use the 5 step method to find the greatest common factor of the following polynomial: 3x3 + 6x2 – 12x

3x3 + 6x2 – 12x Trinomial Variables: x3, x2, and x 1. What do we know? Trinomial Variables: x3, x2, and x Coefficients: 3, 6, and -12

3x3 + 6x2 – 12x Largest number that evenly divides each coefficient 3 What must we find? Largest number that evenly divides each coefficient 3 Largest variable that evenly divides each term. X

3x3 + 6x2 – 12x 3 * X = 3X 3. Calculate GCF: Largest number that divides each term

3x3 + 6x2 – 12x 3 * X = 3X 3. Calculate GCF: Largest variable that divides each term

3x3 + 6x2 – 12x 3. Calculate GCF: 3 * X = 3X GCF

3x3 + 6x2 – 12x 4. Rewrite our polynomial 3x(x2 +2x – 4) GCF Factor

3x3 + 6x2 – 12x 5. Check our answer. Multiply GCF through parenthesis: 3x(x2 +2x – 4) = 3x3 + 6x2 – 12x THEY MATCH!!

Is this important? Used for simplification in later use Assists with graphing in later use Finding similarities of objects (as previously discussed)

Quick Review GCF: Greatest monomial that is a factor of each term of a polynomial. 5 steps: Know, Find, Calculate, Rewrite, Check (KFC & RC)