Long division of polynomials

Question

Hi, 

 

I keep trying to solve this but its confusing. The method i usually do it is by putting 0s as a placeholder where needed. But when im trying to solve the following, when i have to subtract i keep getting zero and i dont know what to do. 

 

(x⁵ - 2x³ -3x² +9) / ( x² -2) 

Answer 1

(x⁵-2x³-3x²+9)/(x²-2)

 

          x³ - 3

        _________________

x²-2/   x⁵ - 2x³ - 3x² + 9        Multiply by x³ to make the x² = x⁵

       -(x⁵-2x³)                       Subtract from the original

      ----------------------

                    -3x² + 9          multiply by -3 to make x² = -3x²

                 -(-3x² + 6)         subtract from previous line

                 ---------------

                               3        remainder = 3

 

Your division is done when the order, or highest exponent, of the

difference is less than the order of the terms being divided by

 

Your answer is   x³ - 3 + 3/(x²-2)

Answer 2

               x³-3

    x² -2 ⌋ x⁵ - 2x³ -3x² +9

               x⁵- 2x³

           --------------

                       -3x²   

                       -3x² +6 

                     --------------

                           -6 +9 =3  remainder