Chapter 8.8, Problem 4LC

To determine

To write: The expressions representing the dimensions of the prism.

Explanation of Solution

Given information:

The volume of the rectangular prism is $36x^3+36x^2+8x$

Formula used:

The volume of the rectangular prism $=\text{length}\times \text{width}\times \text{height}$

Calculation:

Factorize $36x^3+36x^2+8x$

  $\begin{array}{l}36x^3+36x^2+8x\\ =4x(9x^2+9x+2)\\ =4x(9x^2+6x+3x+2)\\ =4x\left(3x(3x+2)+(3x+2)\right)\\ =4x(3x+1)(3x+2)\end{array}$

So, the volume of the rectangular prism $=4x(3x+1)(3x+2)$

Hence, the dimensions of the prism are $(3x+1),(3x+2),4x$