1. ## Cubic equations!

I have been given this question for my maths class, and would appreciate some help. This is the full question.

A different pool at the complex, is constructed within a hole which has a volume equal to 12x^3 + 20x^2 - 81x - 14m^3, and the depth represented by (x - 2) m.
Find the width and length of the hole in terms of x.

Let me explain a bit more, the current assignment is you work for a pool complex and have to find the measurments for the holes required to put in a hole. I need to find out the length and width which I have been given the depth and the equation to do. I have learnt nothing about cubics before and have done as little as quadratics. If you need more info feel free to ask.

2. Factorise the expression.

volume = height * width * depth = $\displaystyle 12x^3 + 20x^2 - 81x - 14 = (x-2)(ax+b)(cx+d)$

Find the other two factors (ax+b), (cx+d).

One way to do this is to divide the original expression by the known factor (x-2), which will give you a quadratic expression. You can factorise the quadratic expression using the quadratic formula or any other method you have been taught.

Note
There may be easier ways to do this if the question has given you hints about the relationship between depth, width, height.

You can deduce the factors quickly if you are allowed to assume that all the coefficients are integers (as it happens, the correct answer does have integer values of a,b,c,d).

3. Originally Posted by cycloneash
I have been given this question for my maths class, and would appreciate some help. This is the full question.

A different pool at the complex, is constructed within a hole which has a volume equal to 12x^3 + 20x^2 - 81x - 14m^3, and the depth represented by (x - 2) m.
Find the width and length of the hole in terms of x.

Let me explain a bit more, the current assignment is you work for a pool complex and have to find the measurments for the holes required to put in a hole. I need to find out the length and width which I have been given the depth and the equation to do. I have learnt nothing about cubics before and have done as little as quadratics. If you need more info feel free to ask.

I suggest you ask your teacher why s/he has given you an assignment on material you have "learnt nothing about" .....

And does this assignment based on material you have "learnt nothing about" count towards your final grade?

4. Yes, this is a graded assignment, that we have to try and teach ourselves something new, and I couldn't quite figure it out, but thanks to SpringFan25 I was able to complete it

5. Thread closed, in accordance with Rule # 6. It is forum policy not knowingly to help with any graded assignments. Next time, do not ask a question that counts towards your final grade.

Thank you.

6. Originally Posted by cycloneash
Yes, this is a graded assignment, that we have to try and teach ourselves something new, and I couldn't quite figure it out, but thanks to SpringFan25 I was able to complete it
I assume you will be giving appropriate acknowledgement of this help on the solution you hand in to your instructor.