Question

Given the expression V = x³ + 16x² + 81x + 126 for the volume of a rectangular prism, find an expression for the missing dimensions?

Answer 1

The rectangular prism's missing dimensions are
`x^2` for the length,
`x + 16`for the width, and
`9x + 14` for the height.

To solve this problem

V = l, w, and h is a general formula for a rectangular prism's volume.

Where:

• the prism's length, breadth, and height are represented by the variables l, w, and h, respectively.

By factoring the provided expression, we can express x in terms of these dimensions. First, determine the common factor (in this example, 1):

`V = x^3 + 16x^2+ 81x + 126`

`V=x^2 (x+16)+9(9x+14)`

Now, we can express
`x`in terms of the dimensions:

`x^2 =length`

`x +16 =width`

`9x+14=height`

So, The rectangular prism's missing dimensions are
`x^2`for the length,
`x + 16` for the width, and
`9x + 14` for the height.