x + 1 minus StartFraction 4 Over x cubed + 3 x squared + 8
Step-by-step explanation:
Volume of the prism is given by the product of its base area and height. To get the height, divide the volume by the base area
Perform long division of the volume polynomial by the polynomial for base area to get the polynomial for height
x³+3x²+8 √x⁴+4x³+3x²+8x+4
-x⁴+3x³+8x
---------------------------
1x³+3x²+0+4
- 1x³+3x²+8
------------------------
-4
The answer will be : x+1 + -4/(x³+3x²+8)
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Dividing polynomials : https://brainly.com/question/11792208
Keywords : volume, rectangular prism, area,height
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The required quotient will be expressed as [tex]x+1 + \frac{-4}{x^33x^2+8}[/tex]
The formula for calculating the volume of a rectangular prism is expressed as:
V = Base area * height
Given the following parameters:
Volume = x^4 + 4x^3 + 3x^2 + 8x + 4
Base area = x^3 + 3x^2 + 8
The formula for calculating the height is expressed as
h = V/B
Using the synthetic division to get the polynomial for height
x³+3x²+8 √x⁴+4x³+3x²+8x+4
-x⁴+3x³+8x
--------------------------
1x³+3x²+0+4
- 1x³+3x²+8
------------------------
-4
Hence the required quotient will be expressed as:
[tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8} = x+1 + \frac{-4}{x^33x^2+8}[/tex]
Learn more on volume of rectangular prism here: https://brainly.com/question/24284033
