EXAMPLE 2 In-Class Example 2 Find three consecutive even integers such that the sum of the smaller two is one-fourth the product of the second and third integers. Answer: 0, 2, 4 or 2, 4, 6 Use your newly updated procedure box to solve. YOU TRY 2 Twice the sum of three consecutive odd integers is fi ve less than the product of the two larger integers. Find the numbers. Solution Step 1: Read the problem carefully, and identify what we are being asked to fi nd. We must fi nd three consecutive odd integers. Step 2: Choose a variable to represent an unknown, and defi ne the other unknowns in terms of the variable. x the first odd integer x 2 the second odd integer x 4 the third odd integer Step 3: Translate the information that appears in English into an algebraic equation. Read the problem slowly and carefully, breaking it into small parts. Statement: Twice the sum of three consecutive odd integers is 5 less than the product of the two larger integers. T T Equation: 2 Cx (x 2) (x 4)D (x 2)(x 4) 5 Step 4: Solve the equation. 2 Cx (x 2) (x 4)D (x 2)(x 4) 5 2(3x 6) x2 6x 8 5 Combine like terms; distribute. 6x 12 x2 6x 3 Combine like terms; distribute. 0 x2 9 Write in standard form. 0 (x 3)(x 3) Factor. x 3 0 or x 3 0 Set each factor equal to zero. x 3 x 3 Solve. Step 5: Check the answer, and interpret the solution as it relates to the problem. We get two sets of solutions. If x 3, then the other odd integers are 1 and 1. If x 3, the other odd integers are 5 and 7. Check these numbers in the original statement of the problem. 2C3 (1) 1D (1)(1) 5 2(3 5 7) (5)(7) 5 2(3) 1 5 2(15) 35 5 6 6 30 30 Find three consecutive odd integers such that the product of the smaller two is 15 more than four times the sum of the three integers. 3 Solve Problems Using the Pythagorean Theorem Recall that a right triangle contains a 90 angle. We can label it as shown in the fi gure. The side opposite the 90 angle is the longest side of the triangle and is called the hypotenuse. The other two hypotenuse c b (leg) a (leg) 90° 434 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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