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b) k2 k 56 The coeffi cient of k is 1, so we can think of this trinomial as k2 1k 56. Find two integers whose product is 56 and whose sum is 1. Since the last term in the trinomial is negative, one of the integers must be positive and the other must be negative. Try to fi nd these integers mentally. Two numbers with a product of positive 56 are 7 and 8. We need a product of 56, so either the 7 is negative or the 8 is negative. Factors of 56 Sum of the Factors 7 8 56 7 8 1 The numbers are 7 and 8: k2 k 56 (k 7)(k 8). Check: (k 7)(k 8) k2 8k 7k 56 k2 k 56 ✓ c) To factor r2 7r 9, fi nd the two integers whose product is 9 and whose sum is 7. We are looking for two positive numbers. Factors of 9 Sum of the Factors 1 9 9 1 9 10 3 3 9 3 3 6 There are no such factors! Therefore, r2 7r 9 does not factor using the methods we have learned here. We say that it is prime. Note We say that trinomials like r2 7r 9 are prime if they cannot be factored using the method presented here. In later mathematics courses, you may learn how to factor such polynomials using other methods so that they are not considered prime. YOU TRY 1 Factor, if possible. a) s2 5s 66 b) d 2 6d 10 c) x2 12x 27 2 More on Factoring a Trinomial of the Form x2 bx c Sometimes it is necessary to factor out the GCF before applying this method for factoring trinomials. 368 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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