Find the quotient when x^3+x^2-x-1 is divided by x-1

X^3 + x^2 - x-1

= x^2 (x+1) - (x+1)

= (x^2-1) (x+1)

[As a^2 - b^2 = (a-b) (a+b) ]

= (x+1) (x-1) (x+1)

Now, { (x+1) (x+1) (x-1) } / (x-1)

= (x+1) (x+1)

So, when x^3 + x^2 - x - 1 is divided by (x-1), the quotient is (x+1) (x+1).