Factoring for partial fraction decompostion

Robb
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Homework Statement


I am trying to factor a denominator so I can do a partial fraction decomposition to solve using a Laplace transform.
denominator= 2s^3+3s^2-3s-2

Homework Equations

The Attempt at a Solution

 
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Robb said:

Homework Statement


I am trying to factor a denominator so I can do a partial fraction decomposition to solve using a Laplace transform.
denominator= 2s^3+3s^2-3s-2

Homework Equations

The Attempt at a Solution


You can guess obvious solutions, for example s = 1 is a root, then use Horner or Euclidean division
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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