Question

Divide (x^3+2x^2-x-2) by (x-1)

Answer 1

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