WEB 2.0

Adv. Algebra I: Factoring Polynomials

• Previously, you learned to...
• • used properties of exponents to evaluate and simplify expressions.
• • added and subtracted polynomials by combining like terms.
• • multiplied polynomials.
• Now, you will study
• • greatest common factors.
• • how to factor polynomials.
• • how to factor special products.
• • how to choose a factoring method

Chapter 7 Lesson 1

• Greatest Common Factor
• Greatest Common Factor
• PRIME FACTORIZATION AND GREATEST COMMON FACTORS

Warm-Up

• 
• Caption: FACTORS AND GREATEST COMMON FACTORS
• YOU HAVE FIVE (5) MINUTES TO COMPLETE THE WARM-UP ACTIVITY.
• ANSWERS:
• 1. NO
• 2. YES
• 3. +/- 1, +/-2, +/-4, +/-7, +/-14, +/-28
• 4. PRIME
• 5. COMPOSITE

OBJECTIVES

• WRITE THE PRIME FACTORIZATION OF NUMBERS
• FIND THE GCF OF MONOMIALS

VOCABULARY

• PRIME FACTORIZATION
• GREATEST COMMON FACTOR

prime factorization

• The numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. You can use the factors of a number to write the number as a product.
• The number 12 can be factored several ways:
• 1*12 2*6 3*4 1*4*3 2*2*3
• The order of the factors does not change the product, but there is only one example above that cannot be factored further. The highlighted factorization is the prime factorization because all the factors are prime numbers. The prime factors can be written in any order, and, except for changes in the order, there is only one way to write the prime factorization of a number

Example 1. Writing Prime Factorizations

• WRITE THE PRIME FACTORIZATION OF 60.
• USE THE FACTOR TREE
• 60
• / \
• 2 * 30
• / \
• 10 * 3
• / \
• 2 * 5
• 60 = 2*2*3*5
• WRITE THE PRIME FACTORIZATION OF EACH NUMBER.
• 1. 98
• 2. 33
• 3. 49
• 4. 19

greatest common factors

• Factors that are shared by two or more whole numbers are called common factors. The greatest of these common factors is called the greatest common factor , or GCF.
• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 32: 1, 2, 4, 8, 16, 32,
• Common factors: 1, 2, 4
• The greatest common factor is 4.

Example 2 Finding GCF of numbers

• Find the GCF of each set of numbers.
• A. 24 AND 60
• METHOD 1: LIST THE FACTORS
• 24: 1, 2, 3, 4, 6, 8, 12, 24
• 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 60
• The GCF of 24 and 60 is 12
• B. 18 AND 27
• METHOD 2: PRIME FACTORIZATION
• 18: 2*3*3
• 27: 3*3*3
• 3*3 = 9
• The GCF of 18 and 27 is 9
• Find the GCF of each set of numbers.
• 1. 12 AND 16
• 2. 5 AND 50
• 3. 26 AND 52
• 4. 100 AND 60

Example 3 Finding GCF of monomials

• Find the GCF of each pair of monomials.
• A. 3x^3 and 6x^2
• 3x^3: 3*x*x*x
• 6x^2: 2*3*x*x
• 3*x*x = 3x^2
• The GCF of 3x^3 and 6x^2 is 3x^2
• B. 4x^2 and 5y^3
• 4x^2: 2*2* x*x
• 5y^3: 5* y*y*y
• The GCF of 4x^2 and 5y^3 is 1
• Find the GCF of each pair of monomials.
• 1. 18g^2 and 32g
• 2. 16a^5 and 9b
• 3.15x^3 and 18x^3

Slide 11

• 
• Factors/Factoring/GCF
• Caption: complete the flowchart

EXIT SLIP