Question

The volume of a rectangular prism box can be represented by the function V(x) = 2x3 − 5x2 − 3x. If the height of the box is x cm, which of the following can represent the length and width of the container? 2x + 1 and x + 3 2x + 1 and x − 3 2x − 1 and x + 3 2x − 1 and x − 3

Answer 1

Explanation:

The volume of a rectangular prism can be represented by the function V(x) = 2x^3 - 5x^2 - 3x, where x is the height of the box in centimeters. We need to determine which of the given options can represent the length and width of the container. To find the length and width, we can divide the volume equation by the height (x). This gives us the following equation: V(x)/x = (2x^3 - 5x^2 - 3x)/x Simplifying this equation gives us: V(x)/x = 2x^2 - 5x - 3 Now, we can factor this quadratic equation to find the length and width. The factorization of 2x^2 - 5x - 3 can be written as: (2x + 1)(x - 3) So, the length and width of the container can be represented by (2x + 1) and (x - 3). Therefore, the correct option is 2x + 1 and x - 3.