The volume of a rectangular prism is open paren x to the 4th power plus 4 x cubed plus 3 x squared plus 8 x plus 4 close paren , and the area of its base is open paren x cubed plus 3 x squared plus 8 close paren If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answer
A
x plus 1 plus the fraction with numerator 4 and denominator x to the 4th power plus 4 x cubed plus 3 x squared plus 8 x plus 4
B
x plus 1 minus the fraction with numerator 4 and denominator x cubed plus 3 x squared plus 8
C
x plus 1 plus the fraction with numerator 4 and denominator x cubed plus 3 x squared plus 8
Explanation
The height is the volume divided by the base area: (x⁴ + 4x³ + 3x² + 8x + 4) ÷ (x³ + 3x² + 8). Polynomial division gives a quotient of x + 1 and a remainder of −4, so the height is x + 1 − 4/(x³ + 3x² + 8). This matches choice B.
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