Question

The volume of a box is (x^3-1)ft^3, and the height is (x- 1) ft What polynomial represents the area of the bottom? The area of the bottom is given by ft^2

Answer 1

Volume of a box  =  (x^3-1)ft^3

Height  =  (x- 1) ft 

Volume  =  Lengrh X Breadth X Height ------------- > (1)

Substitute correspondin values in Eq (1)

(x^3-1)ft^3  =  (x- 1) X Breadth X Height 

Breadth X Height  =  (x^3-1) / (x- 1)

Area  =  (x-1)(x^2 + x + 1) / (x- 1)                [ Since a^3 - b^3  =  (a - b)(a^2 + ab + b^2) ]

Area  =  (x^2 + x + 1) ft^2

Answer :

Area  =  (x^2 + x + 1) ft^2