May Owen
08/02/2024 · Middle School

\( a^{2}-2 a-3 \) entre \( a+1 \)

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Para realizar la división del polinomio \( a^{2} - 2a - 3 \) entre \( a + 1 \), podemos usar la división sintética o la división larga de polinomios. Aquí, usaré la división larga. 1. **Dividimos el primer término del dividendo por el primer término del divisor**: \[ \frac{a^2}{a} = a \] 2. **Multiplicamos el divisor \( a + 1 \) por \( a \)**: \[ a(a + 1) = a^2 + a \] 3. **Restamos este resultado del dividendo**: \[ (a^2 - 2a - 3) - (a^2 + a) = -2a - a - 3 = -3a - 3 \] 4. **Repetimos el proceso**. Ahora dividimos el primer término del nuevo polinomio \( -3a - 3 \) por el primer término del divisor \( a + 1 \): \[ \frac{-3a}{a} = -3 \] 5. **Multiplicamos el divisor \( a + 1 \) por \(-3\)**: \[ -3(a + 1) = -3a - 3 \] 6. **Restamos este resultado**: \[ (-3a - 3) - (-3a - 3) = 0 \] No hay residuo, por lo que la división es exacta. El resultado de la división de \( a^{2} - 2a - 3 \) entre \( a + 1 \) es: \[ a - 3 \]

Quick Answer

El resultado de la división es \( a - 3 \).
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