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SOLUTION

x 2 + 5 x + 6. x 2 + 6 x + 6. x 2 + 6 x. x 2 + 6. C. B. D. A. Area = length width. EXAMPLE 6. Standardized Test Practice. The dimensions of a rectangle are x + 3 and x + 2. Which expression represents the area of the rectangle ?. SOLUTION.

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SOLUTION

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  1. x2 + 5x + 6 x2 + 6x + 6 x2 + 6x x2 + 6 C B D A Area = length width EXAMPLE 6 Standardized Test Practice The dimensions of a rectangle are x + 3 and x + 2. Which expression represents the area of the rectangle? SOLUTION Formula for area of a rectangle = (x + 3)(x + 2) Substitute for length and width. =x2 + 2x + 3x + 6 Multiply binomials.

  2. ANSWER The correct answer is B. B A D C CHECK You can use a graph to check your answer. Use a graphing calculator to display the graphs of y1=(x + 3)(x + 2) and y2=x2 + 5x + 6 in the same viewing window. Because the graphs coincide, you know that the product of x + 3 and x + 2 is x2 + 5x + 6. EXAMPLE 6 Standardized Test Practice = x2 + 5x + 6 Combine like terms.

  3. • Write a polynomial that represents the area of the skateboard park. What is the area of the park if the walkway is 3 feet wide? • Solve a multi-step problem EXAMPLE 7 SKATEBOARDING You are designing a rectangular skateboard park on a lot that is on the corner of a city block. The park will have a walkway along two sides. The dimensions of the lot and the walkway are shown in the diagram.

  4. Area=lengthwidth Solve a multi-step problem EXAMPLE 7 SOLUTION STEP1 Write a polynomial using the formula for the area of a rectangle. The length is 45–x. The width is 33 – x. Formula for area of a rectangle = (45 – x)(33 – x) Substitute for length and width. = 1485 – 45x – 33x + x2 Multiply binomials. = 1485 – 78x + x2 Combine like terms.

  5. ANSWER The area of the park is1260square feet. Solve a multi-step problem EXAMPLE 7 STEP2 Substitute 3 for x and evaluate. Area= 1485 – 78(3) + (3)2 = 1260

  6. The dimensions of a rectangle are x + 5 and x + 9. Which expression represents the area of the rectangle? x2 + 45 x2 + 14x + 45 x2 + 45x + 45 x2 + 45x C A D B C 7 ANSWER C for Examples 6 and 7 GUIDED PRACTICE

  7. for Examples 6 and 7 GUIDED PRACTICE 8. GARDEN DESIGN You are planning to build a walkway that surrounds a rectangular garden, as shown. The width of the walkway around the garden is the same on every side.

  8. ANSWER 4x2 + 38x + 90 ANSWER 306 ft2 for Examples 6 and 7 GUIDED PRACTICE a. Write a polynomial that represents the combined area of the garden and the walkway. b. Find the combined area when the width of the walkway is 4 feet.

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