Note The order in which the factors are written does not matter. In this example, (x 3)(x 4) (x 4)(x 3). b) To factor p2 9p 14, fi nd two integers whose product is 14 and whose sum is 9. Since 14 is positive and the coeffi cient of p is a negative number, 9, both integers will be negative. Factors of 14 Sum of the Factors 1 (14) 1 (14) 15 2 (7) 2 (7) 9 The numbers are 2 and 7. So, p2 9p 14 ( p 2)( p 7). Check: ( p 2)( p 7) p2 7p 2p 14 p2 9p 14 ✓ c) w2 w 30 The coeffi cient of w is 1, so we can think of this trinomial as w2 1w 30. Find two integers whose product is 30 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 30 are 5 and 6. We need a product of 30, so either the 5 is negative or the 6 is negative. Factors of 30 Sum of the Factors 5 6 5 6 1 The numbers are 5 and 6. Therefore, w2 w 30 (w 5)(w 6). Check: (w 5)(w 6) w2 6w 5w 30 w2 w 30 ✓ d) To factor a2 3a 54, fi nd two integers whose product is 54 and whose sum is 3. Since the last term in the trinomial is negative, one of the integers must be positive and the other must be negative. Find the integers mentally. First, think about two integers whose product is positive 54: 1 and 54, 2 and 27, 3 and 18, 6 and 9. One number must be positive and the other negative, however, to get our product of 54, and they must add up to 3. Factors of 54 Sum of the Factors 6 9 6 9 3 6 (9) 6 (9) 3 The numbers are 6 and 9: a2 3a 54 (a 6)(a 9). The check is left to the student. SECTION 7.2 Factoring Tr www.mhhe.com/messersmith inomials of the Form x2 bx c 401
messersmith_power_introductory_algebra_1e_ch4_7_10
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