Question

realiza los siguientes divisiones(x³+4x²-6x-5)÷(x+5)​

Answer 1

Respuesta

$x^2-x-1$

Paso a paso

$\mathrm{Simplificar}\:\frac{\left(x^3+4x^2-6x-5\right)}{\left(x+5\right)}:\quad x^2-x-1$

$\frac{x^3+4x^2-6x-5}{x+5}$

$\mathrm{Factorizar}\:x^3+4x^2-6x-5:\left(x+5\right)\left(x^2-x-1\right)$

$x^3+4x^2-6x-5$

$=\left(x+5\right)\frac{x^3+4x^2-6x-5}{x+5}$

$=\left(x+5\right)\frac{x^3+4x^2-6x-5}{x+5}:\quad x^2-x-1$

$\frac{x^3+4x^2-6x-5}{x+5}$

$=x^2+\frac{-x^2-6x-5}{x+5}$

$=x^2-x+\frac{-x-5}{x+5}$

$=x^2-x-1$

$=\left(x+5\right)\left(x^2-x-1\right)$

$=\frac{\left(x+5\right)\left(x^2-x-1\right)}{x+5}$

$\mathrm{Eliminar\:los\:terminos\:comunes:}\:x+5$

$=x^2-x-1$