YOU TRY 1 Find the greatest common factor of y5 and y8. EXAMPLE 2 In-Class Example 2 Find the greatest common factor for each group of terms. a) 36k4, 28k9, 20k8 b) 56a8b, 21a10b3 c) 20x5y4, 60y2, 50x3y Answer: a) 4k4 b) 7a8b c) 10y Find the greatest common factor for each group of terms. a) 24n5, 8n9, 16n3 b) 15x10y, 25x6y8 c) 49a4b5, 21a3, 35a2b4 Solution a) The GCF of the coeffi cients, 24, 8, and 16, is 8. The smallest exponent on n is 3, so n3 is part of the GCF. The GCF is 8n3. b) The GCF of the coeffi cients, 15 and 25, is 5. The smallest exponent on x is 6, so x6 is part of the GCF. The smallest exponent on y is 1, so y is part of the GCF. The GCF is 5x6y. c) The GCF of the coeffi cients is 7. The smallest exponent on a is 2, so a2 is part of the GCF. There is no b in the term 21a3, so there will be no b in the GCF. The GCF is 7a2. Complete the example on your own and notice the two-step process. YOU TRY 2 Find the greatest common factor for each group of terms. a) 18w6, 45w10, 27w5 b) 14hk3, 18h4k2 c) 54c5d 5, 66c8d 3, 24c2 2 Factor Out the Greatest Common Monomial Factor Earlier we said that to factor an integer is to write it as the product of two or more integers. To factor a polynomial is to write it as a product of two or more polynomials. Throughout this chapter, we will study different factoring techniques. We will begin by discussing how to factor out the greatest common factor. EXAMPLE 3 In-Class Example 3 Factor out the greatest common factor from 4c 28. Answer: 4(c 7) Factor out the greatest common factor from 3y 15. Solution We will use the distributive property to factor out the greatest common factor from 3y 15. First, identify the GCF of 3y and 15: The GCF is 3. Then, rewrite each term as a product of two factors with one factor being 3. 3y 15 (3)( y) (3)(5) 3( y 5) Distributive property When we factor 3y 15, we get 3(y 5). We can check our result by multiplying. 3( y 5) 3 y 3 5 3y 15 390 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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