Question

The volume of a cube is given by the polynomial p(x) = x3 6 x2 + 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.

Answer 1

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.