i need help on an algebra 2 question on dividing polynomials?

Question

my algebra 2 teacher is not the best-- he just can't teach and almost all of my class fails every test because so. anyways, I'm a little perplexed on one question we've got to do for homework:

"Divide. write your answer in fraction form."

(2x^5 - 15x^3 - 9x^2 +11x + 12) / (x + 2)

the way i've been taught, we're supposed to do long division. i've gotten so far as to reaching 2x^4 -2x^3 for my answer but I just know it's got to be wrong. if anyone can help, it'd truly open my eyes a lot more.

Answer 1

                                2x^4 - 4x^3   - 7x^2     +  5x   + 1        +      10/(x+2)

                             --------------------------------------------------------------------

                x + 2    | 2x^5 + 0x^4   - 15x^3    - 9x^2   +11x  + 12

                                2x^5  + 4x^4

                             --------------------------

                                          - 4x^4  - 15x^3

                                          - 4x^4  -  8x^3

                                        -------------------------

                                                        - 7x^3    - 9x^2

                                                        - 7x^3    -14x^2

                                                       ------------------------

                                                                         5x^2   + 11x

                                                                        5x^2    + 10x

                                                                     ------------------------

                                                                                         x       +  12

                                                                                        x        +    2

                                                                                     -------------------------

                                                                                                        10

Answer 2

It is impossible, using this editor, to write the steps to answer this question.

You do this kind of division in EXACTLY the same way you do numerical long division.

I will write the answer I get...maybe that will give you a clue.

2x⁴ - 4x³ - 7x² + 5x + 1, remainder 10

Remember that there is no term in x⁴ in the dividend!!!!

Also remember that the remainder is equal to the dividend evaluated at x=-2.

Answer 3

2x⁴ + 4x³ + 7x² + 5x + 1

x + 2 | 2x⁵ + 0x⁴ - 15x³ - 9x² + 11x + 12

2x⁵ + 4x⁴

1. - 4x⁴ - 15x³

4x⁴ - 8x³

1. - 7x³ - 9x²
2. + 7x³ + 14x²

5x² + 11x

5x² + 10x

x + 2

x + 2

12