The area of a rectangular athletic field is represented by the expression 48x^4 + 32x^3 - 72x square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense Òlength times widthÓ) of the athletic field. Include correct units with your solution.

I got 8x(6x^3 + 4x^ -9)

I'm still not sure how to include correct units. Please help!

To include correct units, you should multiply the length times the width to represent the area of the athletic field. Let's call the length of the field L and the width W.

The area of a rectangle is given by the formula: Area = Length × Width.

Now, let's represent the length and width using algebraic expressions. We'll use L = 8x and W = (6x^3 + 4x - 9).

Multiplying these together, we get:

Area = L × W
= (8x) × (6x^3 + 4x - 9)
= 48x^4 + 32x^2 - 72x.

So, the algebraic expression to represent one possible set of dimensions of the athletic field is: (8x) × (6x^3 + 4x - 9). The units for the area would be square meters, as stated in the question.

To include correct units in the algebraic expression, we need to recognize that the given expression represents the area of the athletic field, which is measured in square meters.

Let's break down the given expression: 48x^4 + 32x^3 - 72x

The expression can be factored out to get the common factors between the terms:
48x^4 can be written as 8x * 6x^3
32x^3 can be written as 8x * 4x^2
-72x remains the same

Putting it all together, we can write the expression as:
8x(6x^3 + 4x^2 - 9)

Now we have an algebraic expression that represents the area of the athletic field. However, we still need to include the units. The units, in this case, are square meters as mentioned before.

So, the final algebraic expression representing the area of the athletic field, including units, is:
8x(6x^3 + 4x^2 - 9) square meters