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con el metodo de ruffini factorizar el ejercicio 

The given polynomial \( f(x) = x^5 - 15x^4 + 85x^3 - 225x^2 + 274x - 120 \) can be factored as:

\[
f(x) = (x - 5)(x - 4)(x - 3)(x - 2)(x - 1)
\]

This shows that the roots of the polynomial are \( x = 1, 2, 3, 4, 5 \), which can be found using Ruffini's method (synthetic division).

Do you want further details on the factorization process or any other specific question? Here are some related questions you might find useful:

1. How is Ruffini's method applied in synthetic division?
2. What are the steps to finding the roots of a polynomial using trial and error?
3. Can any higher-degree polynomial be factored using synthetic division?
4. How do we confirm that these roots are correct?
5. What other factorization methods can be applied to this polynomial?

**Tip**: After finding the roots, it's always useful to verify by expanding the factored form to check if it matches the original equation.

Factorizar el polinomio f(x) = x^5 - 15x^4 + 85x^3 - 225x^2 + 274x - 120 usando el método de Ruffini.

Aprende a factorizar el polinomio f(x) = x^5 - 15x^4 + 85x^3 - 225x^2 + 274x - 120 utilizando el método de Ruffini. Descubre los conceptos fundamentales del álgebra y el proceso de encontrar las raíces polinómicas paso a paso. Ideal para estudiantes de secundaria.

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