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messersmith_power_introductory_algebra_1e_ch4_7_10

The coefficient of the squared term must be 1 before you complete the square! EXAMPLE 1 In-Class Example 1 Complete the square for each expression to obtain a perfect square trinomial. Then, factor. a) n2 12n b) t 2 16t Answer: a) n2 12n 36; (n 6)2 b) t 2 16t 64; (t 8)2 Complete the square for each expression to obtain a perfect square trinomial. Then, factor. a) k2 10k b) p2 8p Solution a) Find the constant needed to complete the square for k2 10k. Step 1: Find half of the coeffi cient of k: 1 2 (10) 5 Step 2: Square the result: 52 25 Step 3: Add 25 to k2 10k: k2 10k 25 The perfect square trinomial is k2 10k 25. The factored form is (k 5)2. b) Find the constant needed to complete the square for p2 8p. Step 1: Find half of the coeffi cient of p: 1 2 (8) 4 Step 2: Square the result: (4)2 16 Step 3: Add 16 to p2 8p: p2 8p 16 The perfect square trinomial is p2 8p 16. The factored form is ( p 4)2. YOU TRY 1 Complete the square for each expression to obtain a perfect square trinomial. Then, factor. a) w2 2w b) r2 18r At the beginning of the section and in Example 1, we saw the following perfect square trinomials and their factored forms. We will look at the relationship between the constant in the factored form and the coeffi cient of the linear term. Perfect Square Trinomial Factored Form x2 6x 9 (x 3)2 3 is 1 2 (6) d 2 14d 49 (d 7)2 7 is 1 2 (14) k2 10k 25 (k 5)2 5 is 1 2 (10) p2 8p 16 ( p 4)2 t2 3t 9 4 4 is 1 2 (8) 3 2 1 2 at 3 2 2 b is (3) 614 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith


messersmith_power_introductory_algebra_1e_ch4_7_10
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