Factoring for partial fraction decompostion

In summary, factoring for partial fraction decomposition is a method used in algebra to simplify rational expressions by breaking them down into simpler fractions. The steps for factoring for partial fraction decomposition involve factoring the denominator, writing the expression as a sum of simpler fractions, setting up a system of equations, solving for unknown coefficients, and simplifying the fractions. This method is useful for simplifying complex rational expressions and finding the roots of polynomial equations, but there are restrictions such as the denominator being factorable and the degree of the numerator being less than the degree of the denominator. It can also be used for improper fractions, but simplification may be necessary.
  • #1
Robb
225
8

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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  • #2
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
 

What is factoring for partial fraction decomposition?

Factoring for partial fraction decomposition is a method used in algebra to simplify rational expressions. It involves breaking down a rational expression into smaller, simpler fractions.

What are the steps for factoring for partial fraction decomposition?

The steps for factoring for partial fraction decomposition are as follows:
1. Factor the denominator of the rational expression.
2. Write the expression as a sum of simpler fractions, with each fraction having a single term in the numerator and a factor of the denominator.
3. Set up a system of equations using the coefficients of the fractions.
4. Solve the system of equations for the unknown coefficients.
5. Plug in the values for the coefficients and simplify the fractions.

Why is factoring for partial fraction decomposition useful?

Factoring for partial fraction decomposition allows us to simplify complex rational expressions, making them easier to work with and solve. It also helps us to find the roots of polynomial equations.

Are there any restrictions when using factoring for partial fraction decomposition?

Yes, there are a few restrictions when using factoring for partial fraction decomposition. The denominator of the rational expression must be factorable, and all factors must be linear or quadratic. Additionally, the degree of the numerator must be less than the degree of the denominator.

Can factoring for partial fraction decomposition be used for improper fractions?

Yes, factoring for partial fraction decomposition can be used for improper fractions. However, the resulting fractions may have a degree higher than the original improper fraction, so simplification may be necessary.

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