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messersmith_power_intermediate_algebra_1e_ch4_7_10

YOU TRY 3 Factor completely. a) x2 15xy 54y2 b) 3k3 18c k2 21c2k If we are asked to factor each of these polynomials, 3x2 18x 24 and 3x2 10x 8, how do we begin? How do the polynomials differ? The GCF of 3x2 18x 24 is 3. To factor, begin by taking out the 3. We can factor using what we learned earlier. 3x2 18x 24 3(x2 6x 8) Factor out 3. 3(x 4)(x 2) Factor the trinomial. In the second polynomial, 3x2 10x 8, we cannot factor out the leading coeffi cient of 3. Next, we will discuss two methods for factoring a trinomial like 3x2 10x 8 where we cannot factor out the leading coeffi cient. 4 Factor ax2 bx c 1a 12 by Grouping Sum is 10 T To factor 3x2 10x 8, fi rst fi nd the product of 3 and 8. Then, fi nd two integers Product: 3 8 24 whose product is 24 and whose sum is 10. The numbers are 6 and 4. Rewrite the middle term, 10x, as 6x 4x, then factor by grouping. 3x2 10x 8 3x2 6x 4x 8 3x(x 2) 4(x 2) Take out the common factor from each group. (x 2)(3x 4) Factor out (x 2). 3x2 10x 8 (x 2)(3x 4) Check: (x 2)(3x 4) 3x2 4x 6x 8 3x2 10x 8 ✓ Notice that the two numbers we are trying to find are factors of the product of a and c whose sum is b. EXAMPLE 4 Factor completely. a) 10p2 13p 4 b) 5c2 29cd 6d 2 Solution a) Sum is 13 T 10p2 13p 4 Product: 10 4 40 Think of two integers whose product is 40 and whose sum is 13. (Both numbers will be negative.): 8 and 5 Rewrite the middle term, 13p, as 8p 5p. Factor by grouping. Be mindful of the signs! 10p2 13p 4 10p2 8p 5p 4 2p(5p 4) 1(5p 4) Take out the common factor from each group. (5p 4)(2p 1) Factor out (5p 4). Check: (5p 4)(2p 1) 10p2 13p 4 ✓ 370 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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