Word problem Polynomialf(x)

1. Sep 28, 2011

Nelo

1. The problem statement, all variables and given/known data

A rectangular shipping container that the Food Bank uses to store their tinned food, has a volume of 2500 cm3. The container is 4 times as wide as it is deep, and 5cm taller than it is wide. What are the dimensions of the container

2. Relevant equations

3. The attempt at a solution

(x)(4x)(4x+5)

= 4x^3 + 20x^2 .

Usually when it asks for dimensions it wants the roots, However i went from factored to expanded, so wth am i supposed to do? cant use bionomial theorem b/c already know the facotred form, etc.

Help?

2. Sep 28, 2011

Nelo

any1?

3. Sep 28, 2011

Mute

You have an expression for the volume: (x)(4x)(4x+5 cm), where x is in cm. What this expression says is that if you specify the depth of the container, x, you can figure out the volume. You don't know the depth, though - what you know is the volume, so you have the reverse problem. The volume given is 2500 cm^3, so your task is to find the depth x such that

2500 cm^3 = (x)(4x)(4x+5 cm)

4. Sep 28, 2011

Nelo

yes, I understand what it is saying.. But what is my next step?

Or do i just combine the first two ? 16x^2 + 20x

Then use quadratic? or factor out? x(16x + 20 )

Idk..

5. Sep 28, 2011

Mute

It's a cubic equation. You can't use the quadratic formula. You have to solve the equation:

16x^3 + (20 cm)x^2 - 2500 cm^3 = 0

There's no nice-and-easy cubic formula that you can use to solve this. One way to solve it would be using a calculator or computer. However, perhaps you learned some tricks in class to try and solve cubic equations with integer coefficients? It turns out the relevant solution to the equation is rather simple.

6. Sep 28, 2011

verty

Simplify the cubic equation into the form x^2 (...) = ..., I found it easier in that form.

7. Sep 28, 2011

Staff: Mentor

I don't see how this is helpful, since the right side won't be zero.

8. Sep 28, 2011

Nelo

Ive tried solving it and i get 16x^3 + (20 cm)x^2 - 2500 cm^3 , but there is simply no factors that will make the eq = 0, so i cant use bionomial theorem. does it mean its not solveable without technology?

9. Sep 28, 2011

eumyang

To make the coefficients a little bit more manageable, factor out the G.C.F. Then use the rational roots theorem. You'll find one integer root that is positive. The other two roots are complex.

And what is this bionomial theorem that you speak of? Never heard of it.