1. ## Polynomials Division

Hello,

I'm taking Algebra II (Saxon), and am completely stuck when it comes to dividing polynomials. I don't know how many times I've read the chapter in the textbook over and over again, trying to somehow figure out what I'm supposed to do.. but I just can't seem to get it.

For example:

(4x^3-3) / (x+2)

Okay, so I write it out like this

______________
x+2) 4x^3 - 3

Now I'm supposed to mentally change the signs, and add..... I'm stuck already. I completely cannot see the connection between the example in the book, and the explanation it gives me.

Could anybody explain this to me?? I would REALLY appreciate it.. I need to finish this stuff tonight..

2. Originally Posted by beckers99
Hello,

I'm taking Algebra II (Saxon), and am completely stuck when it comes to dividing polynomials. I don't know how many times I've read the chapter in the textbook over and over again, trying to somehow figure out what I'm supposed to do.. but I just can't seem to get it.

For example:

(4x^3-3) / (x+2)

Okay, so I write it out like this

______________
x+2) 4x^3 - 3

Now I'm supposed to mentally change the signs, and add..... I'm stuck already. I completely cannot see the connection between the example in the book, and the explanation it gives me.

Could anybody explain this to me?? I would REALLY appreciate it.. I need to finish this stuff tonight..
The process is very similar to a long division problem with numbers. Think of this as being similar to $\displaystyle \frac{4003}{12}$.

Code:
    ______________________
x+2| 4x^3 + 0x^2 + 0x - 3
Now, how many times does x (the first term of "x+2") go into 4x^3? 4x^2 times:
Code:
     __4x^2________________
x+2| 4x^3 + 0x^2 + 0x - 3
Now multiply x+2 by 4x^2 and write it in the space below the polynomial:
Code:
      _4x^2________________
x+2| 4x^3 + 0x^2 + 0x - 3
4x^3 + 8x^2
Now subtract the two lines:
Code:
      __4x^2________________
x+2| 4x^3 + 0x^2 + 0x - 3
-4x^3 - 8x^2
-8x^2
Now bring down the 0x:
Code:
       __4x^2________________
x+2| 4x^3 + 0x^2 + 0x - 3
-4x^3 - 8x^2
-8x^2 + 0x
How many times does x go into -8x^2? -8x times:
Code:
        __4x^2 - 8x____________
x+2| 4x^3 + 0x^2 + 0x - 3
-4x^3 - 8x^2
-8x^2 + 0x
Then:
Code:
          __4x^2 - 8x__________
x+2| 4x^3 + 0x^2 + 0x - 3
-4x^3 - 8x^2
-8x^2 + 0x
-8x^2 -16x
Subtract:
Code:
           __4x^2 - 8x__________
x+2| 4x^3 + 0x^2 + 0x - 3
-4x^3 - 8x^2
-8x^2 + 0x
8x^2 +16x
16x - 3
And again like before:
Code:
           __4x^2 - 8x + 16______
x+2| 4x^3 + 0x^2 + 0x - 3
-4x^3 - 8x^2
-8x^2 + 0x
8x^2 +16x
16x - 3
-16x -32
-35
So $\displaystyle \frac{4x^3 - 3}{x+2} = 4x^2 - 8x + 16 - \frac{35}{x + 2}$

-Dan

3. thank you so much! I think I understand it now!