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 $\displaystyle \frac{4003}{12}$.

Rewrite your first step as:

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