Bradley Lawson
01/06/2024 · Middle School

b) \( 9 x^{2}+6 x+1 \) entre \( 3 x+1 \)

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Para resolver el problema de encontrar el cociente y el residuo de la división de \( 9x^2 + 6x + 1 \) entre \( 3x + 1 \), utilizaremos la división polinomial. Aquí te explico los pasos: 1. **Dividir el término de mayor grado del dividendo por el término de mayor grado del divisor:** \[ \frac{9x^2}{3x} = 3x \] 2. **Multiplicar el divisor por el cociente obtenido y restar el resultado del dividendo:** \[ (3x)(3x + 1) = 9x^2 + 3x \] \[ 9x^2 + 6x + 1 - (9x^2 + 3x) = 3x + 1 \] 3. **Observar que el término resultante es igual al divisor, lo que indica que no hay más términos de mayor grado en el dividendo:** \[ 3x + 1 = 3x + 1 \] Por lo tanto, el cociente es \( 3x \) y el residuo es \( 0 \). Resumen: \[ \frac{9x^2 + 6x + 1}{3x + 1} = 3x + \frac{0}{3x + 1} \] El cociente es \( 3x \) y el residuo es \( 0 \).

Quick Answer

El cociente es \( 3x \) y el residuo es \( 0 \).
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