9. What is the quotient of (x3 + 2x2 - x+6) + (x + 3)?

x^3 + 2x^2 - x + 6

Step-by-step explanation:

Please write that as x^3 + 2x^2 - x + 6, where the " ^ " indicates exponentiation.  

Use synthetic division to determine whether or not (x + 3) is a factor of x^3 + 2x^2 - x + 6.  If you don't know synthetic division, then divide x^3 + 2x^2 - x + 6 by x + 3 using long division.

Using synthetic division:

Identify the coefficients of this x^3 + 2x^2 - x + 6:  They are 1, 2, -1 and 6.

Set up synthetic division:

-3     /   1    2    -1    6

                -3     3   -6

           1     -1      2    0

Because the remainder is zero, we now know that (x + 3) is a factor and that the quoitient is

1x^2 - x + 2

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.