Question

The volume of a rectangular prism (shown below) is 12x⁵−27x³. What are the dimensions of the prism? Show all work.

a) 3x²x(4x³-3)
b) 3x²x(4x²-3)
c)3x²x(2x³-9)
d)3x²x(2x²-9)

Answer 1

The dimensions of the rectangular prism are x³, 3, and 4x²−9.

Step-by-step explanation:

To find the dimensions of the rectangular prism, we need to factor the volume expression. The volume of the prism is given by 12x⁵−27x³. We can factor out the common factor x³ from both terms:

12x⁵−27x³ = x³(12x²−27)

Then, we can further factor the expression inside the parentheses by factoring out the common factor 3:

12x²−27 = 3(4x²−9)

So, the factored form of the volume expression is x³(3)(4x²−9).

The dimensions of the prism can be obtained by equating the factors to the respective dimensions. The length is given by x³, the width is given by 3, and the height is given by 4x²−9.

Therefore, the dimensions of the prism are x³, 3, and 4x²−9.