Question

Divide 9x^2-21x-20 by x-1

Answer 1

$9 x^{3}-30 x^{2} +x+20$

Answer 2

Answer:

1) quotient:  9x - 12
2) remainder: - 32

Explanation:

I will use short division, which consists in using just the coefficients.

This is the full operation:

  literal            x^2      x         0
 coefficient   | 9      - 21     - 20
                    |
                 1 |            9       - 12
                 -------------------------------------
                      9      -12      - 32

Result:

1) quotient:  9x - 12
2) remainder: - 32

You can prove the result by multiplyin (9x - 12) times (x - 1) and then adding  the remainder (-32).

=> (9x - 12) (x - 1) - 32 = 9x^2 - 9x - 12x + 12 - 32 = 9x^2 - 21x - 20 which proves the answer.