Final answer:
To find the missing dimension of a rectangular prism with a given polynomial volume expression, factor the polynomial and find its linear components. The missing dimension is one of these components, or it can be found by dividing the volume by the product of the known dimensions if they are available.
Step-by-step explanation:
To find the missing dimension of a rectangular prism with the given volume V = 2x^3 + 17x^2 + 46x + 40, we first need to express this volume as a product of its dimensions, which are typically length, width, and height for a rectangular prism. I assume that the prism's dimensions are factors of the volume polynomial. The process of factoring this polynomial may be complex, requiring seeking combinations of numbers that both add to the coefficients of the terms and multiply to yield the constant term. Once factored completely, the missing dimension would be one of the linear factors.
In practical terms, if we know two dimensions of the prism, we can determine the third dimension by dividing the volume by the product of the known dimensions. If the volume expression is not easily factored, numerical methods or algebraic software may be used to approximate or find the root which represents the missing dimension.