Question

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

Answer 1

yes

Explanation:

Answer 2

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).