Most airlines have rules concerning the size of checked baggage. The rules for Budget Airline are such that the dimensions of the largest bag cannot exceed 45 in. by 55 in. by 62 in. A designer is drawing plans for a piece of luggage that athletes can use to carry their equipment. It will have a volume of 76,725 cubic Inches. The length is 10 in. greater than the width and the depth is 14 in. less than the width. What are the dimensions of this piece of luggage? 1. Write an equation in factored form to model the volume of the piece of luggage. 2. Multiply and set the equation equal to zero. 3. Think about possible roots of the equation. Could a root be a multiple of 42 a multiple of 5? a multiple of 10? How do you know? 4. Use synthetic substitution to test possible roots. Choose positive integers that are factors of the constant term and reasonable in the context of the problem. (This is a synthetic division table) Possible Root 1 -140 -76.725 5. Which equation represents the factored polynomial? A (W+55)(w2 + 25W + 1550) = 0 B (W - 35)(W2 + 60W + 1405) = 0 C (w - 45)(w2 + 41w1705) = 0 D (W - 4)(W2 140w +76.725) = 0 6 Which could be the dimensions of this piece of luggage? A 31 in. by 45 in. by 55 in. B 45 in. by 55 in. by 55 in. C 45 in. by 45 in. by 55 in. D 45 in. by 55 in. by 62 in