# Homework Help: Factoring Cubic Polynomials/Function

1. Mar 6, 2010

### CursedAntagonis

1. The problem statement, all variables and given/known data
Doing my vector mechanics dynamics homework and I cannot believe I am stuck on this part.

trying to factor

t^3 - 6t^2-36t - 40 = 0

2. Relevant equations

3. The attempt at a solution
I honestly do not remember where to begin. I remember there is a formula for perfect cubes, but do not remember what is needed for this situation. Any tips is greatly appreciated.

2. Mar 6, 2010

### Chewy0087

There is a formula but it's nasty and you could always just try Newton-Raphson method for the first factor then long division?

3. Mar 6, 2010

### vela

Staff Emeritus
You can find all the factors of 40 to try guess how the polynomial factors. Generally, though, I find plotting the function is the quickest way of finding its roots, at least for homework problems.

4. Mar 6, 2010

### jlazarow

Easy way is to find one root and divide the cubic by it.

i.e. in this situation you can see -2 is a root, so divide the polynomial by t+2, then factor the result to get the other roots.

5. Mar 6, 2010

### Mentallic

If the problem were changed to +36t, then you would be able to factorize by using the perfect cube.
You would end up having $(t-6)^3+176=0$ and then you could use the sum of two cubes formula to factorize further (or even just solve the equation for t directly).

But this is not the case

6. Mar 10, 2010