Question

Determine the volume of one rectangiular prism v(x)=54x^3+264x^2-738x+420 ?

Answer 1

We have 
v(x)=54x^3+264x^2-738x+420 , and the sum of coefficients are
54+264-738+420=0, so 1 is a zero of v(x), it means v(1)=0
so v(x) can be written as v(x)= (x-1) Q(x)
and obviously, Q(x) = v(x) / (x-1)
Q(x)=54x^3+264x^2-738x+420/(x-1)= (6x+42)(9x-10)
v(x)=(x-1)(6x+42)(9x-10)

the volume of rectangular prism is V= LxWxH
we can assume tha L=x-1, W=6x+42 and H= 9x-10