How can I factor a cubic equation?

Thread starter luv2smile
Start date Sep 22, 2009
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Cubic Factoring

In summary, factoring a cubic equation is the process of breaking down a cubic polynomial into its simplest form to find its roots. This is important because it allows us to solve for the roots and simplify complex expressions. The steps for factoring a cubic equation include finding the GCF, checking if it is a perfect cube, using the quadratic formula or other methods, and writing the final factored form. However, not all cubic equations can be factored, and in these cases, other methods may be used. Factoring a cubic equation has many real-world applications, such as finding optimal solutions, predicting behavior, and solving mathematical models in various fields.

Sep 22, 2009

luv2smile

Homework Statement

g(x)= x^4-2x^3-3x^2+2x+2

Homework Equations

The Attempt at a Solution

After using synthesized division, got
x^3-x^2-4x-2

I need help in factoring from here please

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Sep 22, 2009

symbolipoint

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I would try binomial divisors of (x+1), (x-1), (x+2), and (x-2).

Sep 22, 2009

Bohrok

The reason for the choice of the factors above are from the http://en.wikipedia.org/wiki/Rational_root_theorem" , in case you were wondering.

Last edited by a moderator: May 4, 2017

Sep 24, 2009

luv2smile

Thank you for the help!

Related to How can I factor a cubic equation?

1. What is factoring a cubic equation?

Factoring a cubic equation is the process of breaking down a cubic polynomial into its simplest form by finding its factors. This allows us to solve the equation and find its roots.

2. Why is factoring a cubic equation important?

Factoring a cubic equation is important because it helps us solve for the roots of the equation, which can provide valuable information about the behavior and solutions of the equation. It also allows us to simplify complex expressions and make them easier to work with.

3. What are the steps for factoring a cubic equation?

The steps for factoring a cubic equation are as follows:
1. Find the greatest common factor (GCF) of the terms in the equation
2. Determine if the equation is a perfect cube
3. Use the quadratic formula or other methods to solve for the remaining factors
4. Check the solution by substituting the factors back into the equation and simplifying
5. Write the final factored form of the equation.

4. Can all cubic equations be factored?

No, not all cubic equations can be factored. Some equations may have irrational or complex roots, making it impossible to factor using real numbers. In these cases, other methods such as the cubic formula or numerical methods may be used to find the solutions.

5. What are some real-world applications of factoring a cubic equation?

Factoring a cubic equation has many real-world applications, including but not limited to:
- Finding the optimal solution for a given problem in fields such as economics, engineering, and physics
- Predicting the behavior of a system or process
- Designing and solving mathematical models
- Simplifying and solving complex equations in chemistry and physics
- Finding the roots of a polynomial function in computer science and coding.