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División sintética de polinomios

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División sintética de polinomios

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Prueba de división sintética

Created by

GLADIS PEÑA
GLADIS PEÑA
Dominican Republic

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División sintética de polinomios
 

División sintética de polinomiosOnline version

Prueba de división sintética

by GLADIS PEÑA
1

¿Qué se utiliza para dividir un polinomio por (x - c) en división sintética?

2

¿Qué se obtiene como primer valor en la fila de resultados al realizar división sintética?

3

¿Qué representa el residuo en la división sintética?

4

Si se divide P(x) por (x-3) y el residuo es 0, ¿qué conclusiones se pueden sacar?

5

¿Qué ocurre si c se toma como un valor que no es raíz de P(x) durante la división sintética?

6

¿Qué representa el cociente obtenido en la división sintética cuando P(x) es de grado n y se divide por (x-c)?

7

¿Qué signo se usa en el divisor para la división sintética típica?

8

¿Qué herramienta se utiliza para reducir el cálculo en divisiones grandes?

9

Si P(x)=2x^3+3x^2-x+5 y queremos dividir por (x-1), ¿qué corresponde al primer cociente término?

10

¿Qué condición garantiza que (x-c) sea factor de P(x) usando división sintética?

Explicación

La división sintética usa los coeficientes, no el valor de c directamente.

Se empieza con el coeficiente líder del polinomio original.

El residuo es el valor del polinomio evaluado en x=c.

Residuo 0 indica que 3 es raíz de P(x).

Si c no es raíz, el residuo no será cero.

El cociente tiene grado uno menos que P(x).

La forma estándar es (x - c).

La división sintética simplifica procesos con coeficientes.

El primer cociente tiene el grado una menos que P, así 2x^3 -> 2x^2.

Residuo 0 implica que (x-c) es factor de P(x).

 
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