CHAPTER_ppt_6_1

# CHAPTER_ppt_6_1 - Chapter 6 Factoring Polynomials 6.1 The...

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Chapter 6 Factoring Polynomials

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§ 6.1 The Greatest Common Factor and Factoring by Grouping
Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Factors Factors (either numbers or polynomials) When an integer is written as a product of integers, each of the integers in the product is a factor of the original number. When a polynomial is written as a product of polynomials, each of the polynomials in the product is a factor of the original polynomial. Factoring – writing a polynomial as a product of polynomials

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Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Greatest common factor – largest quantity that is a factor of all the integers or polynomials involved. Finding the GCF of a List of Integers or Terms 1) Write each number as a product of prime numbers. 2) Identify the common prime factors. 3) The product of all common prime factors found in step 2 is the greatest common factor. If there are no common prime factors, the greatest common factor is 1. Greatest Common Factor
Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Find the GCF of each list of numbers. 1) 12 and 8 12 = 2 · 2 · 3 8 = 2 · 2 · 2 So the GCF is 2 · 2 = 4. 1) 7 and 20 7 = 1 · 7 20 = 2 · 2 · 5 There are no common prime factors so the GCF is 1.

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