Answer:
the quotient is 1x^2 - 2x + 0, and the remainder is -1.
Explanation:
The polynomial x^3 - x^2 - 2x should be rewritten as x^3 - x^2 - 2x + 0. Recall that a polynomial of order n has n + 1 terms. It just so happens that the polynomial given here has a zero constant term.
If we are to divide x^3 - x^2 - 2x + 0 by x + 1, we must use -1 as the divisor in synthetic division.
Thus, we end up with this synthetic division setup:
-1 / 1 -1 -2 0
-1 2 -1
--------------------------
1 -2 0 -1
Thus, the quotient is 1x^2 - 2x + 0, and the remainder is -1.