Question

the volume of a cube is given by the polynomial p(x)= x^3 -6x^2 +12x -8 find the possible expression for the sides of the cube verify the truth of ur answer when the length is 3cm

Answer 1

Solution:-
p(x) = x³ - 6x² + 12x - 8
= x³ - 3 × 2 × x(x - 2) - 2³
= (x - 2)³
So, side of the cube is x - 2.
Now, when the side of the cube is 3 cm.
Volume of the cube = (3)³ = 27 cu cm
or, x - 2 = 3
x = 3 + 2
x = 5 
And volume is = 5³ - 6*5² + 12*5 - 8
= 125 - 6*15 + 60 - 8
= 125 - 150 + 60 - 8
185 - 158
= 27
Verified.