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messersmith_power_intermediate_algebra_1e_ch4_7_10

YOU TRY 5 Complete the square for each expression to obtain a perfect square trinomial. Then, factor. a) w2 2w b) z2 16z We’ve seen the following perfect square trinomials and their factored forms. Let’s 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 10x 25 (x 5)2 5 is 1 2 (10). c c d2 8d 16 (d 4)2 4 is 1 2 (8). c c y2 6y 9 (d 3)2 3 is 1 2 (6). c c t2 14t 49 (t 7)2 7 is 1 2 (14). c c This pattern will always hold true and can be helpful in factoring some perfect square trinomials. Be sure you understand these relationships before reading Example 6. EXAMPLE 6 Complete the square for n2 5n to obtain a perfect square trinomial. Then, factor. Solution Find the constant needed to complete the square for n2 5n. Step 1: Find half of the coeffi cient of n: 1 2 (5) 5 2 Step 2: Square the result: a5 2 b 2 25 4 Step 3: Add 25 4 to n2 5n. The perfect square trinomial is n2 5n 25 4 . The factored form is an 5 2 b 2 . 5 2 is c 1 2 (5), the coeffi cient of n. Check: an 5 2 b 2 n2 2n a5 2 b a5 2 b 2 n2 5n 25 4 YOU TRY 6 Complete the square for p2 3p to obtain a perfect square trinomial. Then, factor. 618 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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