The volume of a rectangular prism is 24x^3-4x^2-8x. Use factoring to find the three dimensions of the prism

Answer 1

V = 4x(6x² - x - 2) = 4x(3x -2)(2x + 1)

Answer 2

If we want to factor this expression 24x³-4x²-8x, let's first look for the Greatest Common Factor of 24x³, -4x²_,- 8x.

The GCF of the three terms is 4x, so that means we can rewrite the original expression as follows:

24x³ - 4x² - 8x = 4x(6x² - x - 2)

Now, you need to factor the expression *inside* the parentheses: 6x² - x - 2

That can be factored as 6x² - x - 2 = (2x + 1)(3x - 2)

So that means that the original expression can be factored as:

24x³ - 4x² - 8x = 4x(2x + 1)(3x - 2)

Those are the 3 dimensions of your prism.