Question

The volume of a rectangular prism in terms of x is given by

V (x) = x^3 + 3x^2 - 10x - 24.
Given that two sides are x + 2 and x – 3, find the missing side in terms of X.

Answer 1

To find the missing side y of a rectangular prism with given sides x + 2 and x - 3 and volume formula V(x) = x³ + 3x² - 10x - 24, we use the equation y(x + 2)(x - 3) = x³ + 3x² - 10x - 24 and solve for y.

Step-by-step explanation:

The student is asked to find the missing side of a rectangular prism when two sides and the volume are given in terms of x. Given the formula V(x) = x³ + 3x² - 10x - 24, and two sides as x + 2 and x - 3, we can find the missing side by realizing that the volume of the prism is the product of its three dimensions. Therefore, to find the third side, which we can call y, we set up the equation y(x + 2)(x - 3) = x³ + 3x² - 10x - 24 and solve for y. Simplifying both sides of the equation, we can find the value of y in terms of x.