Question

You want the volume of the box to be 2 cubic inches. Find the rational solution(s) of the equation. Then use polynomial long division to find the other solution(s). What are the possible side lengths of the box?

a) 1 inch
b) 2 inches
c) 3 inches
d) 4 inches

Answer 1

The possible side lengths of the box with a volume of 2 cubic inches are 1 inch and 2 inches.

Step-by-step explanation:

To find the possible side lengths of the box with a volume of 2 cubic inches, we will solve a polynomial equation. Let's assume the side lengths of the box are x, y, and z.

The equation for the volume of the box is given by V = xyz = 2.

To find the rational solutions, we can try different values for x, y, and z that satisfy the equation. In this case, we can try:

a) If x = 1 inch, then yz = 2. We can choose y = 2 inches and z = 1 inch, which satisfies the equation.

b) If x = 2 inches, then yz = 1. We can choose y = 1 inch and z = 1 inch, which satisfies the equation.

c) If x = 3 inches, then yz = 2/3. There are no rational values of y and z that satisfy this equation.

d) If x = 4 inches, then yz = 1/2. There are no rational values of y and z that satisfy this equation.

Therefore, the possible side lengths of the box are: a) 1 inch and 2 inches.