e) To factor c2 6c 9, notice that the product, 9, is positive and the sum, 6, is negative, so both integers must be negative. The numbers that multiply to 9 and add to 6 are the same number, 3 and 3: (3) (3) 9 and 3 (3) 6. So c2 6c 9 (c 3)(c 3) or (c 3)2. Either form of the factorization is correct. f ) To factor y2 11y 35, fi nd two integers whose product is 35 and whose sum is 11. We are looking for two positive numbers. Factors of 35 Sum of the Factors 1 35 1 35 36 5 7 5 7 12 There are no such factors! Therefore, y2 11y 35 does not factor using the methods we have learned here. We say that it is prime. Note We say that trinomials like y2 11y 35 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 2 Factor, if possible. a) m2 11m 28 b) c2 16c 48 c) a2 5a 21 d) r2 4r 45 e) r2 5r 24 f ) h2 12h 36 3 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. Note From this point on, the first step in factoring any polynomial should be to ask yourself, “Can I factor out a greatest common factor?” Since some polynomials can be factored more than once, after performing one factorization, ask yourself, “Can I factor again?” If so, factor again. If not, you know that the polynomial has been completely factored. 402 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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