# The volume of the cube is given by polynomial . Find the possible expression for the side of the cube. Verify it when the side of the cube is 3 cm.

1
by rajniDewan

2015-09-18T18:37:25+05:30

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P(x)  = 8 x³ - 36 x² + 54 x - 27
Volume of a cube is a perfect cube of  its side.
By examining the first term  and  the last term of  P(x) we can check if it is a cube of  (2 x  - 3)
=  (2x)³ + 3 * (2x)² (-3) + 3 (2x) (-3)² + (-3)³
=  8 x³ - 36 x²  + 54 x - 27

hence,  the magnitude of the side is given by :  (2x - 3).
when side of the cube is = 2x - 3 = 3 cm
So   x  = (3 + 3) /2 = 3 cm

Substituting in P(x) :   8 (3)³ - 36 (3² ) + 54 (3) - 27
= 216 - 324 + 162 - 27  = 27  cm³

since x³ = 27 cm³,  it verifies.

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