Question

División de polinomios:
1. (x³-x²+x-1): (x²-1)

2.(3x⁴+x³+5x²+x-5): (x²-1)​

Answer 1

Respuesta:

1. $\frac{x^2+1}{x+1}$

2. $=3x^2+10x+32+\frac{87x-37}{x^2-3x+1}$

Explicación paso a paso:

1. Procedimiento:

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

2. Procedimiento :

$\frac{\left(3x^4+x^3+5x^2+x-5\right)}{\left(x^2-3x+1\right)}\\\\\frac{3x^4+x^3+5x^2+x-5}{x^2-3x+1}=3x^2+\frac{10x^3+2x^2+x-5}{x^2-3x+1}\\\\=3x^2+\frac{10x^3+2x^2+x-5}{x^2-3x+1}\\\\\frac{10x^3+2x^2+x-5}{x^2-3x+1}=10x+\frac{32x^2-9x-5}{x^2-3x+1}\\\\=3x^2+10x+\frac{32x^2-9x-5}{x^2-3x+1}\\\\\frac{32x^2-9x-5}{x^2-3x+1}=32+\frac{87x-37}{x^2-3x+1}\\\\=3x^2+10x+32+\frac{87x-37}{x^2-3x+1}$