Question

A rectangular prism has a volume of 16y^4+16^y^3+48y^2 cubic units. Which could be the base area and height of the prism?

Answer 1

`\bf \textit{volume of a rectangular prism}\\\\ V=Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ -----------\\ V=16y^4+16y^3+48y^2 \end{cases} \\\\\\ 16y^4+16y^3+48y^2=Bh\implies 16y^2(y^2+y+3)=Bh`

so since its just two factors, you can pick either for the "B" or "h", or one can say that the trinomial is the "B", because it can be factored into a couple more binomials, either way will work.