# Is this cublc polynomial function solvable?

1. Dec 8, 2012

### davedave

Here is a very difficult cubic polynomial.

x^3 - x - 2 = 0

I am wondering whether it is solvable or not. Please think about it.

2. Dec 8, 2012

### aew782

I need help with this too I posted a similar one and haven't got a response... mine was x^3 + 9x -1=0...They are solvable, but I don't know how to get an answer algebraically or graphically.

3. Dec 8, 2012

### rasmhop

Last edited: Dec 8, 2012
4. Dec 8, 2012

### symbolipoint

Are they solvable? Let's have a guess: The first one can be tested for divisibility by x+1, x-1, x+2, and x-2. The second one can be tested for divisibility by x+1 and x-1. The results may be faster if you know synthetic division.

5. Dec 8, 2012

### aew782

Thank you that's all I needed!

6. Dec 8, 2012

### SteamKing

Staff Emeritus
You can use synthetic division, but isn't it simpler to just evaluate the polynomial and see if the equation is satisfied?

7. Dec 9, 2012

8. Dec 9, 2012

### symbolipoint

The first binomial rendering zero remainder is (x-2). The quotient is x^2+2x+1 which is (x+1)^2. No need to use Cardano's or Vietas substitution for this cubic (micromass gave a good reference Wikipedia article).