Question

The length of a rectangular prism is 1 more than twice the width w. The volume of the prism is 2w^3 + 15w^2 + 7w. What is the simplified expression for the height of the prism?

Answer 1

Do you ever feel like a plastic bag??

Answer 2

When I get problems that I have no idea how to do, then yes

Answer 3

Then, the volume of the prism is:
V = (1+2w)*w*h
But the problem says that V = 2w^3 + 15w^2 + 7w, so
(1+2w)*w*h = 2w^3 + 15w^2 + 7w, let's find h:
(1+2w)*w*h = w*(2w^2 + 15w + 7)
(1+2w)*h = (2w^2 + 15w + 7)
(1+2w)*h = 2*(w+1/2)*(w+7)
(w+1/2)*h = (w+1/2)*(w+7)
h = w+7