Question

What is the standard form polynomial representing the volume of this shipping container?

The image shows a blue shipping container with the numbers:
4×2 + 3x(along the length of the bottom)
x2 – 8 (Along the bottom of the ‘front’)
6x + 15 (going up the length of the ‘front’)

1. The standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 – 147x^3 – 624x^2 – 360x.

### What is a Standard Form Polynomial?

A standard form polynomial is a polynomial expression written whereby the term with the highest degree or power on a variable is written first in the expression, followed by the least, then the constant of the polynomial comes last.
What is the Volume of a Rectangular Prism?
The Volume of a rectangular prism = (length)(width)(height).
The shipping container is a rectangular prism with the following dimensions:
Length of container = 4x² + 3x
Width of container = x² – 8
Height = 6x + 15
Plug in the values
Volume of container = (4x² + 3x)(x² – 8 )(6x + 15)
Expand
Volume of container = 24x^5 + 78x^4 – 147x^3 – 624x^2 – 360x
Thus, using the formula for the volume of a rectangular prism, the standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 – 147x^3 – 624x^2 – 360x.