Given the volume and height, find a polynomial expression for the area of the base in terms of x for each figure.

Question

V=Bh

V(x)=x^4-16

h=x+2

Answer 1

Since V = Bh, B = V/h

     

                           = (x⁴ - 16)/(x + 2)

 

                           = [(x² - 4)(x² + 4)]/(x + 2)

 

                           = [(x+2)(x-2)(x² + 4)]/(x + 2)

 

                           =(x - 2)(x² + 4)

 

                           =x³ - 2x² + 4x - 8