# Can some one explain this question

#### Stouffville

##### New member
An open-topped box can be made from a sheet of aluminium measuring 50 cm by 30 cm by cutting congruent squares from the four corners and folding up the sides. Write a polynomial function to represent the volume of the box, and then use it to determine the dimensions that result in a volume greater than 4000 cm^3
All I got is
V=(x-50)(x-30)(x)
I do not understand what to do after

#### Dr.Peterson

##### Elite Member
An open-topped box can be made from a sheet of aluminium measuring 50 cm by 30 cm by cutting congruent squares from the four corners and folding up the sides. Write a polynomial function to represent the volume of the box, and then use it to determine the dimensions that result in a volume greater than 4000 cm^3
All I got is
V=(x-50)(x-30)(x)
I do not understand what to do after
Please show how you got that equation. It is incorrect.

A labeled picture will help. What will be each dimension of the box?

Once you have the right expression for volume, you can use it to write an inequality, and try to solve it.

#### Subhotosh Khan

##### Super Moderator
Staff member
An open-topped box can be made from a sheet of aluminium measuring 50 cm by 30 cm by cutting congruent squares from the four corners and folding up the sides. Write a polynomial function to represent the volume of the box, and then use it to determine the dimensions that result in a volume greater than 4000 cm^3
All I got is
V=(x-50)(x-30)(x)
I do not understand what to do after
What is 'x'?

#### Stouffville

##### New member
Sorry I got it how is it (50-2x)(30-2x)x. I go how to find the equation but I do not know what to do after.

#### Subhotosh Khan

##### Super Moderator
Staff member
Sorry I got it how is it (50-2x)(30-2x)x. I go how to find the equation but I do not know what to do after.
I ask again - what is 'x'?

#### Dr.Peterson

##### Elite Member
Sorry I got it how is it (50-2x)(30-2x)x. I go how to find the equation but I do not know what to do after.
That's the correct equation, assuming that x is the side of each square. (You really need to define variables before stating equations.)

An open-topped box can be made from a sheet of aluminium measuring 50 cm by 30 cm by cutting congruent squares from the four corners and folding up the sides. Write a polynomial function to represent the volume of the box, and then use it to determine the dimensions that result in a volume greater than 4000 cm^3
Now set your expression equal to 4000 and solve to find when the volume will equal 4000 cm^3. Presumably you have learned something about solving polynomial inequalities, which will be the next step.

Since this is a cubic, it's not easy to factor. I suggest looking for a rational root. Is that something you've learned recently?

#### Stouffville

##### New member
will it be :
(50-2x)(30-3x)x

= 6x^3 - 210x^2 + 1500x

WIll the rational roots be 2/50 or 3/30 because my teacher never taught me about rational root

#### Dr.Peterson

##### Elite Member
will it be :
(50-2x)(30-3x)x

= 6x^3 - 210x^2 + 1500x

WIll the rational roots be 2/50 or 3/30 because my teacher never taught me about rational root
You need to set this equal to 4000, as I said:

6x^3 - 210x^2 + 1500x = 4000​

Now you have to get this all on one side and factor that side.

If you haven't learned about rational roots, then you'll need to tell us what you have learned, or we can't really help you. We have no idea what methods you can use unless you tell us. What topics have been recently covered in class? Are you perhaps allowed to use technology like graphing calculators?

#### Stouffville

##### New member
You need to set this equal to 4000, as I said:

6x^3 - 210x^2 + 1500x = 4000​

Now you have to get this all on one side and factor that side.

If you haven't learned about rational roots, then you'll need to tell us what you have learned, or we can't really help you. We have no idea what methods you can use unless you tell us. What topics have been recently covered in class? Are you perhaps allowed to use technology like graphing calculators?
This is not a school it is a private school for credit of math. But the teacher does not teach at all.

#### Cubist

##### Senior Member
Sorry I got it how is it (50-2x)(30-2x)x
will it be :
(50-2x)(30- 3x )x

Like @Dr.Peterson wrote, your first expression was correct, but then you copied it out incorrectly in the next post with a "3x" (and therefore the subsequent expansion is wrong too)

Last edited:

#### Dr.Peterson

##### Elite Member
This is not a school it is a private school for credit of math. But the teacher does not teach at all.
I didn't ask what kind of school you are in, or whether you have a good teacher. I asked two things: what you yourself are able to do (so we know what methods to suggest); and what is expected in the context of the problem, whatever that may be (so we can know what methods the problem itself might be designed to provide exercise in).
my teacher never taught me about rational root
So what have you been taught? Or rather, perhaps, what is the teacher supposed to have taught? What is the context of the problem (e.g. a certain section of a book, or a certain web page)? What techniques are available for you to learn by studying that context?

With no context, the the only methods I can think of for you to use are rational roots and technology.

will it be :
(50-2x)(30-3x)x

= 6x^3 - 210x^2 + 1500x
To make sure we agree on the equation, it should be

(50-2x)(30-2x)x = 4000​

which expands to

4x^3 - 160x^2 + 1500x - 4000 = 0​

#### Stouffville

##### New member
I have done long divide, some factor themor and reminder themor and that is it

#### Stouffville

##### New member
It too late now I already hand it in with out the answer for this question.

#### Dr.Peterson

##### Elite Member
I have done long divide, some factor theorem and remainder theorem and that is it
It too late now I already hand it in with out the answer for this question.
Those theorems are commonly taught leading up to the rational root theorem, and are part of the work of applying it. Without the RRT, you could at least try dividing by a few small numbers to see if you can find a zero; from that, you could find the others using the factor theorem.

And I hope you at least showed your work as far as you could get.