Question

The formula for volume of this rectangular prism is:

V = 2x^3 + 17x^2 + 46x + 40

Find an expression for the missing side length.

Answer 1

Well the volume of a rectangular prism is:
\(\text{Volume}=\text{length} \times \text{width} \times \text{height}\)

From the diagram, you know:
\(2x^3 + 17x^2 + 46x + 40=(?) \times (x+4) \times (x+2)\)

So what you can do is divide the volume by the [product \( (x+4)(x+2)\). You could proceed by long division to do this, which should give you the last remaining factor (the length).

Answer 2

And by the product I mean when you fully multiply out \((x+4)(x+2)\)

Answer 3

i got x^2 + 6x + 8 would that be right?

Answer 4

@kirbykirby

Answer 5

For the product of those 2 factors, yes. Now the last step is dividing the volume by what you just found to get the length.

Answer 6

Can you help me with the division part? I've always had trouble with it... :D