What are the possible expresssions for the dimensions of the cuboid whose volume is $3 x^{2} - 12 x$ ?

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Solution

Volume $3 x^{2} - 12 x = 3 x (x - 4)$
$∴$ Factors are 3, x, and x - 4
Now if length = 3, breadth = x and height
= x - 4
if length = 3, breadth = x - 4, Height = x
If length = x, breadth = 3, height = x - 4
if length = x, breadth = x - 4, height = 3
if length = x - 4, breadth = 3, height = x
if length = x - 4, breadth = x, height = 3

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