Solution a) If the product of two numbers is positive 15 and the sum of the numbers is positive 8, then the two numbers will be positive. (The product of two positive numbers is positive, and their sum is positive as well.) First, list the pairs of positive integers whose product is 15—the factors of 15. Then, fi nd the sum of those factors. Factors of 15 Sum of the Factors 1 15 1 15 16 3 5 3 5 8 The product of 3 and 5 is 15, and their sum is 8. b) If the product of two numbers is positive 24 and the sum of those numbers is negative 10, then the two numbers will be negative. (The product of two negative numbers is positive, while the sum of two negative numbers is negative.) First, list the pairs of negative numbers that are factors of 24. Then, fi nd the sum of those factors. You can stop making your list when you fi nd the pair that works. Factors of 24 Sum of the Factors 1 (24) 1 (24) 25 2 (12) 2 (12) 14 3 (8) 3 (8) 11 4 (6) 4 (6) 10 The product of 4 and 6 is 24, and their sum is 10. c) If two numbers have a product of negative 28 and their sum is positive 3, one number must be positive and one number must be negative. (The product of a positive number and a negative number is negative, while the sum of the numbers can be either positive or negative.) First, list pairs of factors of 28. Then, fi nd the sum of those factors. Factors of 28 Sum of the Factors 1 28 1 28 27 1 (28) 1 (28) 27 4 7 4 7 3 The product of 4 and 7 is 28, and their sum is 3. In-Class Example 1 Find two integers whose a) product is 16 and sum is 10. b) product is 40 and sum is 13. c) product is 36 and sum is 5. Answer: a) 8 and 2 b) 8 and 5 c) 4 and 9 Follow the approach used in the solution of each example. YOU TRY 1 Find two integers whose a) product is 21 and sum is 10. b) product is 18 and sum is 3. c) product is 20 and sum is 12. Note You should try to get to the point where you can come up with the correct numbers in your head without making a list. SECTION 7.2 Factoring Tr www.mhhe.com/messersmith inomials of the Form x2 bx c 399
messersmith_power_introductory_algebra_1e_ch4_7_10
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