Question

MathPhys! Sqdancefan! Geniuses Please help!

The volume of a triangular prism is given by
`12x^(5)` -
`27^(4)` +
`20x^(3)` -
`x^(2)` -
`127x^{}` +
`63` The height of the prism is given by
`4x - 9`.
Using long polynomial division, find an expression for the area of the base of the triangular prism.

Answer 1

`\boxed{A=3 {x}^(4) + {5x}^(2) + 11x - 7}`

Explanation:

`</p><p>if \: its \: volume \: is \to \: \\ 12x^(5)- 27x^(4) + 20x^(3) - x^(2) - 127x + 63 \\ given \: the \: height \: is \to \\ 4x - 9 \\ then \: the \:a rea \: is \: given \: by \to \\ A= (V)/(h) .............where \: \boxed{v} \: is \: the \: volume \\ A= (12x^(5)- 27x^(4) + 20x^(3) - x^(2) - 127x + 63 )/(4x - 9 ) \to\\ \\ 4x - 9 ) \frac{ \frac{3 {x}^(4) + {5x}^(2) + 11x - 7}{.....................................................} }{ \frac{12x^(5)- 27x^(4) + 20x^(3) - x^(2) - 127x + 63}{ \frac{ - (12x^(5)- 27x^(4)) }{ \frac{ \to \: 20x^(3) - x^(2) - 127x + 63}{ \frac{ -(20x^(3) - 45 {x}^(2) ) }{ \frac{ \to \: 44 {x}^(2) - 127x + 63}{ \frac{ - (44 {x}^(2) - 99x)}{ \frac{ \to \: - 28x + 63}{ \frac{ ( - ( - 28x + 63))/( \to \: 0) }{} } } } } } } } } \\ hence\: the \: area \: is \: given \: to \: be \to \\ \boxed{A=3 {x}^(4) + {5x}^(2) + 11x - 7}`

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