Factoring a Cubic Polynomial: x^3-2x^2-5x+6

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To factor the cubic polynomial x^3 - 2x^2 - 5x + 6, the rational root theorem is suggested as a useful method. A quick factor identified is x - 1. The discussion also touches on the relevance of the polynomial to a characteristic equation for a third-order differential equation. The original poster expresses gratitude for the assistance received. Overall, the focus is on finding the factors of the given cubic polynomial.
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Homework Statement



Factor the equation.

Homework Equations



x^3-2x^2-5x+6

The Attempt at a Solution



Could someone help me know how to factor this equation?
 
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peace-Econ said:

Homework Statement



Factor the equation.

Homework Equations



x^3-2x^2-5x+6

The Attempt at a Solution



Could someone help me know how to factor this equation?

The rational root theorem is a helpful place to start. One factor I found very quickly was x - 1.

BTW, your thread title doesn't seem to have much to do with your question. Is this the characteristic equation for a third-order DE?
 


You're right. I was just working on the characteristic equation. But, I could figure it out. Thank you so much!
 

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