The volume of a cube is given by the polynomial p(x) = x 3 - 6x 2 + 12x -8 . Find the possible expressions for the sides of the cube. Verify the truth of your answer when the length of cube is 3 cm.
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Solution:-
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 of the cube = (3)³
= 27 cu cm
Or, x - 2 = 3
x = 3 + 2
x = 5
Ans volume = 5³ - 6 × 5² + 12 × 5 - 8
= 125 - 150 + 60 - 8
= 185 - 158
= 27 Answer.
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 of the cube = (3)³
= 27 cu cm
Or, x - 2 = 3
x = 3 + 2
x = 5
Ans volume = 5³ - 6 × 5² + 12 × 5 - 8
= 125 - 150 + 60 - 8
= 185 - 158
= 27 Answer.
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4
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