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

2. EXAMPLE 6 = x 2 + 5x + 6 Combine like terms. ANSWER The correct answer is B. A D C B Standardized Test Practice CHECK You can use a graph to check your answer. Use a graphing calculator to display the graphs of y 1 = (x + 3)(x + 2) and y 2 = x 2 + 5x + 6 in the same viewing window. Because the graphs coincide, you know that the product of x + 3 and x + 2 is x 2 + 5x + 6.

3. Skateboarding EXAMPLE 7 Solve a multi-step problem 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. 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 ?

4. SOLUTION EXAMPLE 7 Solve a multi-step problem STEP 1 Write a polynomial using the formula for the area of a rectangle.The length is 45 – x. The width is 33 – x. Area = length width Formula for area of a rectangle = (45 – x)(33 – x) Substitute for length and width. = 1485 – 45x – 33x + x 2 Multiply binomials. = 1485 – 78x + x2 Combine like terms.

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

6. GUIDED PRACTICE for Examples 6 and 7 SOLUTION Area = length width Formula for area of a rectangle = (x + 5)(x + 9) Substitute for length and width. = x 2 + 9x + 5x+ 45 Multiply binomials. x 2 + 45x A x 2 + 45x + 45 D x 2 + 45 B x 2 + 14x + 45 C The dimensions of a rectangle are x + 5 and x + 9. Which expression represents the area of the rectangle ? 7

7. GUIDED PRACTICE for Examples 6 and 7 = x 2 +14x + 45 Combine like terms. ANSWER The correct answer is C. A D C B

8. GUIDED PRACTICE for Examples 6 and 7 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. Garden Design

9. GUIDED PRACTICE for Examples 6 and 7 Write a polynomial using the formula for the area of a rectangle.The length is (2x +9). The width is (2x +10). a Area = length width Formula for area of a rectangle = (2x +9)(2x +10) Substitute for length and width. = 4x 2 + 20x +18x + 90 Multiply binomials. = 4x 2 + 38x + 90 Combine like terms. ANSWER = 4x 2 + 38x + 90

10. GUIDED PRACTICE for Examples 6 and 7 Substitute 4 for y and evaluate. Area = 4(4) 2 + 38(4) 2 + 90= 306 ANSWER Combined area is = 306ft 2 b. Find the combined area when the width of the walkway is 4 feet.