What are the possible polynomial expressions for the dimensions of the cuboids whose volumes are given below?
$3 x^{3} - 12 x$

3 (x - 2) (x + 2)

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3 x (x - 2) (x + 2)

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3 x^{2} (x - 2) (x + 2)

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None of above

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Solution

The correct option is C $3 x (x - 2) (x + 2)$
Given volume of cuboids is $3 x^{3} - 12 x$
The volume of cuboid $= l b h$ $= 3 x (x^{2} - 4)$
We know $x^{2} - y^{2} = (x + y) (x - y)$
$∴ 3 x (x^{2} - 4)$ $= 3 x (x + 2) (x - 2)$
Then dimensions are $3 x, (x + 2)$ and $(x - 2)$ .

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3 x^{2} - 12 x

2 x^{2} + 10 x + 12

What are the possible expressions for the dimensions of the cuboid whose volume is 3x^2-12x

V o l u m e : 3 x^{2} - 12 x

\begin{matrix} \begin{matrix} V o l u m e : 3 x^{2} - 12 x \end{matrix} (i) \end{matrix} \begin{matrix} \begin{matrix} V o l u m e : 12 k y^{2} + 8 k y - 20 k \end{matrix} (i i) \end{matrix}

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