HELP! Dividing Polynomials. Egh!

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Divide (–9x^4 – 24x^3 + 2x^2 + 3x – 1) by (3x + 1).

A. –3x^3 – 7x^2 + 3x – (1 / 3x + 1)
B. –3x^3 – 9x^2 + 1 + (11x^2 - 2 / 3x + 1)
C. –3x^3 + 7x^2 – 3x + 1
D. 3x^3 + 7x^2 – 2 + (1 / 3x + 1)

I set this problem up as long division and I got

-3x^3 - 9x^2 - 7x^2 and then I got lost.

Obviously I did something wrong in the beginning because -7x^2 isn't even an option in the answers. I have no idea what I did and I'm having a hard time understanding this kind of division. If someone could please help, I'd be so grateful!!

Another problem similar to this that I had a problem with was to divide

(x^4 + y^4) by (x^2 - y^2)

How do I solve these problems?!
 
Code: 
            3x^3+9x^2+7x/3-2/9
         ---------------------------------------------
3x+1 | -9x^4-24x^3+2x^2+3x-1
        -9x^4+3x^3
         ---------------------------------
           -27x^3+2x^2+3x-1
           -27x^3+9x^2
                   ------------------------------------
                          -7x^2+3x-1
                          -7x^2+(7x/3)
                            ------------------------------
                                    (2x/3)-1
                                    (2x/3)-2/9
                                        ---------------------------
                                           -7/9

So, you have \(\displaystyle \L\\\frac{7}{9(3x+1)}+3x^{3}+9x^{2}+\frac{7}{3}x-\frac{2}{9}\)
 
Divide (–9x^4 – 24x^3 + 2x^2 + 3x – 1) by (3x + 1).

A. –3x^3 – 7x^2 + 3x – (1 / 3x + 1)
B. –3x^3 – 9x^2 + 1 + (11x^2 - 2 / 3x + 1)
C. –3x^3 + 7x^2 – 3x + 1
D. 3x^3 + 7x^2 – 2 + (1 / 3x + 1)

I set this problem up as long division and I got

-3x^3 - 9x^2 - 7x^2 and then I got lost.

Obviously I did something wrong in the beginning because -7x^2 isn't even an option in the answers. I have no idea what I did and I'm having a hard time understanding this kind of division. If someone could please help, I'd be so grateful!!
------------------------
Code: 
        -3x^3 - 7x^2 + 3x
     ____________________________
3x+1 ) -9x^4 - 24x^3 + 2x^2 + 3x -1
       -9x^4 -  3x^3
       -------------------------------
              -21 x^3 + 2x^2 + 3x - 1
              -21 x^3 - 7x^2
              -------------------------
                        9x^2 + 3x - 1
                        9x^2 + 3x
                        ---------------
                                   - 1
So A is the answer.

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

Another problem similar to this that I had a problem with was to divide

(x^4 + y^4) by (x^2 - y^2)

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

Sorry, I don't have a clue on this one! The denominator will factor into (x+y)(x-y), and the numerator will also factor into (x^2 + xy sqrt(2) + y^2)*(x^2 - xy sqrt(2) + y^2), but there are no factors in common to cancel, so I'm stuck.

Steve
 
-3x^3 - 7x^2 + 3x
____________________________
3x+1 ) -9x^4 - 24x^3 + 2x^2 + 3x -1
-9x^4 - 3x^3
-------------------------------
-21 x^3 + 2x^2 + 3x - 1
-21 x^3 - 7x^2
-------------------------
9x^2 + 3x - 1
9x^2 + 3x
---------------
- 1
So A is the answer.
Click to expand...

Regarding the first line where it says:

- 24x^3
- 3x^3

Why wouldn't the answer to that be -27x^3 instead of -21x^3
 
Code: 
            x^2 + y^2
          .....................
x^2 - y^2 ) x^4      + 0  + y^4
            x^4 - x^2 y^2
            .............
                  x^2 y^2 + y^4
                  x^2 y^2 - y^4
                  .............
                          2 y^4
(x^2 + y^2)(x^2 - y^2) + 2y^4 = x^4 - y^4 + 2y^4 = x^4 + y^4

...hmmm
 
catalinamemday said:
- 24x^3
- 3x^3
Why wouldn't the answer to that be -27x^3 instead of -21x^3
Click to expand...
because you're subtracting;
-24x^3 - (-3x^3) = -24x^3 + 3x^3 = -21x^3
 
Ohh! I completely missed that!

Thank you so much for the help, everyone!

I really appreciate it!!!!!
 
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