Assignment: Factor Trinomials Using Guess and Check Follow the directions to find the missing side lengths in each problem. Be sure to show all work necessary to find your answer. 1. A gardener is planning to plant a rectangular vegetable garden during the spring. The rectangle below represents a plan for the garden with a width of x feet. a. Find the length (l) of the rectangle if the area of the rectangle is 2 x x 12 . (Hint: Factor the trinomial 2 x x 12 0 using the guess and check method.) b. Find the dimensions (length width) and the area of the garden if x = 10 feet. (Hint: Substitute 10 for x in the expressions for length, width, and area.) x l area = 2 x x 12 K12 Inc. 2. A city manager wants to add a playground in a new city park. The rectangle below represents the plan for the dimensions of the rectangular playground. w x + 15 a. Find the width (w) of the rectangle if the area of the rectangle is x2 + 18x + 45. b. Find the dimensions (length width) and the area of the playground if x = 8 yards. area = x2 + 18x + 45 K12 Inc. 3. A construction manager needs to hire workers and order materials for building the foundation of a house. The rectangle below represents the houses foundation. a. Find the length (l) and width (w) of the rectangle if the area of the rectangle is 2 x x 40 300 . b. Find the dimensions (length width) and the area of the foundation if x = 20 feet. 4. Think of another real-world situation involving a rectangle. a. Describe what the rectangle represents and find the dimensions of the rectangle in terms of x, assuming the area is represented by the polynomial 2 x x8 9 . b. Using a specific value for x, find the dimensions (length x width) and area of the rectangle