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Realiza la siguiente división algebraica \( \left(6 x^{2}+13 x+5\right) \div(2 x+1) \)

Ask by Jimenez Klein. in Mexico
Dec 06,2024

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La división algebraica se simplifica a \( 3x+5 \).

Solución

Calculate or simplify the expression \( (6x^2+13x+5)/(2x+1) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(6x^{2}+13x+5\right)}{\left(2x+1\right)}\) - step1: Remove the parentheses: \(\frac{6x^{2}+13x+5}{2x+1}\) - step2: Factor the expression: \(\frac{\left(2x+1\right)\left(3x+5\right)}{2x+1}\) - step3: Reduce the fraction: \(3x+5\) La división algebraica \( \left(6 x^{2}+13 x+5\right) \div(2 x+1) \) se simplifica a \( 3x+5 \).

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Bonus Knowledge

Para realizar la división algebraica \( \left(6 x^{2}+13 x+5\right) \div(2 x+1) \), primero podemos usar la división sintética o larga. Al aplicar la división larga, primero dividimos el término de mayor grado: 1. Dividimos \(6x^2\) entre \(2x\), lo que nos da \(3x\). 2. Multiplicamos \(3x\) por \(2x + 1\) para obtener \(6x^2 + 3x\). 3. Restamos \( (6x^2 + 3x) \) de \( (6x^2 + 13x + 5) \), quedando \(10x + 5\). 4. Repetimos el proceso: dividimos \(10x\) entre \(2x\), obteniendo \(5\). 5. Multiplicamos \(5\) por \(2x + 1\), resultando \(10x + 5\). 6. Restamos, y al final obtenemos el residuo \(0\). Así que \( \left(6 x^{2}+13 x+5\right) \div(2 x+1) = 3x + 5 \) sin residuo.

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