High School

Find the volume of a rectangular prism if the length is \(4x\), the width is \(2x\), and the height is \(x^3 - 3x + 4\).

A. \(8x^6 - 24x^4 + 32x^3\)

B. \(8x^6 - 12x^4 + 4x^3\)

C. \(4x^6 - 6x^4 + 2x^3\)

D. \(4x^6 - 24x^4 + 32x^3\)

Answer :

Final answer:

The volume of the rectangular prism is 8x⁶ - 24x⁴ + 32x³.

Explanation:

The volume of a rectangular prism can be found by multiplying the length, width, and height. In this case, the length is 4x, the width is 2x, and the height is x³-3x+4. So, the volume is given by:

V = (4x) * (2x) * (x³-3x+4)

Expanding and simplifying the expression gives:

V = 8x⁶ - 24x⁴ + 32x³

Therefore, the volume of the rectangular prism is 8x⁶ - 24x⁴ + 32x³.

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