Question

Can someone break this down into steps for me?
The polynomial x^3 + 5x^2 - ­57x -­189 expresses the volume, in cubic inches, of a shipping box, and the width is (x+3) in. If the width of the box is 15 in., what are the other two dimensions? ( Hint: The height is greater than the depth.)

Answer 1

The volume formula for a rectangular box is V = length * width * depth.

Divide the given volume by (x+3). What's left is the product of the length and the height. Hope this info is sufficient to help you solve this problem yourself.

Answer 2

Note: the "width of the box" is given in two different forms: 15 inches and x+3. this seems to imply that you could set these equal to one another and solve for x.

Answer 3

when i did that I got: x^3+5x^2-72x+27... so do i then respectively replace the x with the "15" and solve accordingly? Not sure where I need to go with this

Answer 4

err not 15... but 12

Answer 5

right: x=12. Do you now have enuf info to find the length and height of the box?

Answer 6

You could still divide that "volume," x^3 + 5x^2 - ­57x -­189, by the width, x+3.
Assuming you obtain a quotient without remainder, you could then attempt to factor that quotient. Finally, subst. x=12 in all 3 expressions. First, the width is 15-3 = 12 inches.

Answer 7

I'm not fully understanding what to do with the polynomial after I divide the x+3 out of it.... or what I should be doing with the 12

Answer 8

Divide that x+3 into the polynomial. I'd bet you'll get no remainder.

That means your quotient is the product of the length and the height.

See whether you can factor that quotient.

Last, subst. x=12 in all 3 expressions to obtain length, height and width.

Answer 9

Ok thanks I think i got it now :)

Answer 10

You're welcome!