Question

(2x⁵+x³+3x-2)/(x+1) determinar el cociente y residuo

Answer 1

(2x⁵+x³+3x-2)/(x+1)

$\frac{\left(2x^5+x^3+3x-2\right)}{\left(x+1\right)}$

Dividimos:

$=2x^4+\frac{-2x^4+x^3+3x-2}{x+1}$

$=2x^4-2x^3+\frac{3x^3+3x-2}{x+1}$

$=2x^4-2x^3+3x^2+\frac{-3x^2+3x-2}{x+1}$

$=2x^4-2x^3+3x^2-3x+\frac{6x-2}{x+1}$

$=2x^4-2x^3+3x^2-3x+6+\frac{-8}{x+1}$

Simplificamos:

$=2x^4-2x^3+3x^2-3x+6-\frac{8}{x+1}$

Resultado:

$\boxed{=2x^4-2x^3+3x^2-3x+6-\frac{8}{x+1}} }$