Question

The volume of a filing cabinet can be represented by the expression P(x)=2x3−13x2+26x−15, where x is the height of the cabinet. What are the possible dimensions of the cabinet in terms of x?

Answer 1

To find the possible dimensions of the filing cabinet in terms of x, factorize the expression P(x)=2x^3−13x^2+26x−15 and solve for x. The roots of the expression represent the possible dimensions of the cabinet.

Step-by-step explanation:

The volume of a filing cabinet can be represented by the expression P(x) = 2x^3 - 13x^2 + 26x - 15, where x is the height of the cabinet.

To find the possible dimensions of the cabinet in terms of x, we can factorize the expression.

1. First, find the roots of the expression by setting P(x) = 0 and solving for x using factoring, the quadratic formula, or a graphing calculator.
2. Once you have the roots, the possible dimensions of the cabinet are the values of x that satisfy the problem. For example, if one root is x = 1, then the possible height of the cabinet would be 1.
3. Repeat the process for all the roots to find the possible dimensions of the cabinet in terms of x.