Question

The volume of a rectangular prism is 2x^4- 128x. What are the length of the prism's sides?

Answer 1

• 2x

,

• x-4

,

• x²+4x+16

Explanation:

Given the volume of a rectangular prism:

`V=2x^4-128x`

To determine the side lengths, we factor the expression for V.

`V=2x(x^3-64)=2x(x^3-4^3)`

Next, we factorize x³-4³ using the difference of two cubes rule:

`a^3-b^3=(a-b)(a^2+ab+b^2)`

Therefore:

`x^3-4^3=(x-4)(x^2+4x+4^2)=(x-4)(x^2+4x+16)`

The factored form of V is, therefore:

`V=2x(x-4)(x^2+4x+16)`

The lengths of the prism's sides are 2x, x-4 and x²+4x+16.