Write a polynomial equation to model this situation.

- x^{3} + 12 x^{2} - 47 x + 36

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x^{3} + 12 x^{2} - 47 x + 36

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x^{3} + 12 x^{2} - 47 x - 36

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None of the above

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Solution

The correct option is A $- x^{3} + 12 x^{2} - 47 x + 36$
$Let 'x' be the amount he want to shave off from each dimensions.$
$∴ The volume is$
$V = (3 - x) (4 - x) (5 - x)$
$= (3 - x) (20 - 9 x + x^{2})$
$= 60 - 27 x + 3 x^{2} - 20 x + 9 x^{2} - x^{3}$
$= - x^{3} + 12 x^{2} - 47 x + 60$
$According to question$
$V = 24$
$\Rightarrow - x^{3} + 12 x^{2} - 47 x + 60 = 24$
$\Rightarrow - x^{3} + 12 x^{2} - 47 x + 36 = 0$
Option A is correct.

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