Question

A rectangular box for a new product is designed in such a way that the three dimensions always have a particular relationship defined by the variable x. The volume of the box can be written as 2x^3+17x^2+38x+15, and the height is always x+3. What are the width and length of the box

Answer 1

You can find the product of the width and length by dividing the volume polynomial by the height, \(x+3\).

Via synthetic division, you have
\[\begin{array}{c|cccc}
-3&2&17&38&15\\
&&-6&-33&-15\\
\hline
&2&11&5&0
\end{array}\]
which means
\[\frac{2x^3+17x^2+38x+15}{x+3}=2x^2+11x+5=\text{width}\times\text{length}\]
You'll never be able to find the precise width and length of the box, but I'll bet the question assumes you can and expects you to factor this polynomial further (which can be done).