FInd expressions for the possible dimensions of the rectangular prism? V=3y^3+16y^2+5y

Question

How do I solve this problem?

Answer 1

The dimensions of a rectangular prism are length, width, and depth.

Volume = length * width * depth

Here, V = 3y³ + 16y² + 5y. If you can factor that into three terms, those could be the dimensions of the prism.

How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.

V = y(3y² + 16y + 5)

Then, factor what's left.

V = y(3y + 1)(y + 5)

The dimensions of the prism are y, (3y + 1), and (y + 5).