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4. Aplicar la división de polinomios en los siguientes ejercicios; \( \begin{array}{ll}\text { A. }\left(3 x^{3}-5 x^{3}+x-2\right) \div(x+2) & \text { B. }\left(2 x^{3}+4 x-3 x^{2}-2\right) \div(2 x+1) \\ \text { 5. Simplificar las expresiones indicadas y expresar los resultados con expone }\end{array} \)

Ask by Turnbull Bryant. in Colombia
Mar 09,2025

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**Ejercicio A:** \[ \frac{3x^3 - 5x^3 + x - 2}{x + 2} = -2x^2 + 4x - 7 + \frac{12}{x + 2} \] **Ejercicio B:** \[ \frac{2x^3 + 4x - 3x^2 - 2}{2x + 1} = x^2 - 2x + 3 - \frac{5}{2x + 1} \]

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¡Vamos a sumergirnos en la división de polinomios! Para el ejercicio A, primero debes simplificar el polinomio, combinando los términos similares: \(3x^{3} - 5x^{3} = -2x^{3}\), entonces el polinomio se vuelve \(-2x^{3} + x - 2\). Luego, puedes proceder a dividirlo entre \(x + 2\) utilizando la regla de Ruffini o el método de división larga. Ahora, en el ejercicio B, debes reordenar los términos para facilitar la visualización: \(2x^{3} - 3x^{2} + 4x - 2\) es tu nuevo polinomio a dividir entre \(2x + 1\). Al igual que en el caso anterior, la división larga o Ruffini te ayudará a llegar al cociente y, si es necesario, un residuo. ¡Dividir polinomios puede ser un rompecabezas matemático emocionante!

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