Factoring a polynomial where factor theorem doesn't work

[adrimare]

Homework Statement

Solve: x^3 - 9x^2 + 15x + 30

Homework Equations

The Attempt at a Solution

The factors of 30 are +-1, +-2, +-3, +-5, +-6, +-10, +-15, and +-30.

I used my graphing calculator and got a zero close to -1. I plugged it into the original equation and got 5, not 0. I used the zero function on my calculator and found that the zero occurred around -1.13. that's a fraction.

How would I solve this algebraically?

 

[talolard]

Try Newtons method:
Define
$$T(x)=x-\frac{f(x)}{f'x}=x-\frac{x^3-9x^2+15x+30}{3x^2+18x+15}$$

 

[gabbagabbahey]

If you are only looking for a numerical approximation, then Newton's method should work fine for you. However, if you are looking for an exact analytical solution, try the cubic formula