find the possible expression of the dimensions of a cuboid whose volume is x³-23x²+142x-120 cubic units
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Given : The volume of a cube is given by the polynomial
p(x) = x3 - 6x2 + 12x - 8 = x3 - 23 - 3 × 2 × x(x - 2) = (x - 2)3
⇒ Side of the cube = x - 2
Now, When the side of the cube = 3 cm
Volume = (3 cm)3 = 27 cm3
or x - 2 = 3
⇒ x = 3 + 2 = 5
and volume = 53 - 6 × 52 + 12 × 5 - 8 = 125 - 150 + 60 - 8 = 27
Step-by-step explanation:
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