Question

Determine o
quociente de x4+x3-7x2+9x-1
por =x2+3x-2 e verifique
se possui resto.

Answer 1

Olá, Cornetta.

$\frac{x^4+x^3-7x^2+9x+1}{}|\frac{x^2+3x-2}{}$

$\frac{x^4+x^3-7x^2+9x+1}{-x^4-3x^3+2x^2}|\frac{x^2+3x-2}{x^2}$

$\frac{-2x^3-5x^2+9x+1}{}|\frac{x^2+3x-2}{x^2-2x}$

$\frac{-2x^3-5x^2+9x+1}{2x^3+6x^2-4x}|\frac{x^2+3x-2}{x^2-2x}$

$\frac{x^2+5x+1}{}|\frac{x^2+3x-2}{x^2-2x}$

$\frac{x^2+5x+1}{}|\frac{x^2+3x-2}{x^2-2x+1}$

$\frac{x^2+5x+1}{-x^2-3x+2}|\frac{x^2+3x-2}{x^2-2x+1}$

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

Portanto:

$\boxed{\frac{x^4+x^3-7x^2+9x+1}{\underbrace{2x+3}_\text{{resto}}}|\frac{x^2+3x-2}{\underbrace{x^2-2x+1}_{\text{quociente}}}}$