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

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SUMMARY

The cubic polynomial x^3 - 2x^2 - 5x + 6 can be factored using the Rational Root Theorem. A confirmed factor is (x - 1). This factorization simplifies the polynomial and aids in solving related equations. The discussion also touches on the relevance of the polynomial in the context of characteristic equations for third-order differential equations.

PREREQUISITES
  • Understanding of polynomial functions
  • Familiarity with the Rational Root Theorem
  • Basic algebraic manipulation skills
  • Knowledge of characteristic equations in differential equations
NEXT STEPS
  • Study the Rational Root Theorem in detail
  • Learn how to factor higher-degree polynomials
  • Explore solving characteristic equations for differential equations
  • Practice factoring various cubic polynomials
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Students studying algebra, particularly those focusing on polynomial factorization and differential equations, will benefit from this discussion.

peace-Econ
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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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