Question

The measure of the volume of a rectangular solid is 5x^3-20x 2x^2-8. find the measures of the dimensions of the solid if each one can be written as a binomial with integral coefficients?

Answer 1

The measures of the dimensions of the rectangular solid are (5x + 2), (x + 2), and (x - 2).

Step-by-step explanation:

To find the measures of the dimensions of the rectangular solid, we can factor the given volume expression: 5x^3 - 20x + 2x^2 - 8. Rearranging the terms, we get (5x^3 + 2x^2) - (20x + 8). Now, we can factor out common terms from each parenthesis: x^2(5x + 2) - 4(5x + 2). We can see that (5x + 2) is a common factor. Factoring it out, we have (5x + 2)(x^2 - 4). The dimensions of the solid can be represented as (5x + 2), (x + 2), and (x - 2).