Can somebody help me to understand how to divide polynomials?

Question

such as (x+1)/(2x^2-7x^2-3x-5)

either explain it here or im me. THANKS!!!

Answer 1

Dividing polynomials is like dividing numbers, but with the places held by powers of x, rather than 10. In your case, you need to combine the first two terms first. You get something like -5x^2 -3x - 5 divided by x+1. If these were positive signs, then it would be 5x^2+3x+5 divided by x+1. This is just like dividing 535 by 11, except that you don't carry or borrow from place to place, and trial division by the first term is exact, not approximate. It would be like this division:

5 -2 <------ quotient 5 not 4, as 1 goes into 5 5 times and this is exact
11 | 5 3 5
5 5
---------
-2 5 <------Subtraction results in negative number, not in borrowing
-2 -2
--------
7

Now put the x's back in and you have division of polynomials.

I note that Yahoo makes a mess out of my formatting, so you have to straighten it out.

Answer 2

It seems you've misconstrued the problem. It probably should be (2x^2-7x^2-3x-5)/(x+1).

Now are you sure it's "2x^2"? If it is, you need to combine like terms, so the problem becomes:
(-5x^2-3x-5)/(x+1).

Since I don't have the formatting to do this like I would on paper, I'll describe the operation:
Divide -5x^2-3x by x+1; place -5x over -3x; multiply x+1 by -5x and place the result under the -5x^2-3x and subtract to determine the difference, remembering the sign rules. (The result is -5x^2-5x; the difference is 2x.) Now bring down the -5 next to the 2x, and divide this number by x+1. Each time you do this, you want the first term to be used up. 2x-5 divided by x+1 is 2. Now multiply the x+1 times 2, to get 2x+2. Subtract 2x+2 from 2x-5. When you adjust the signs, you end up with a remainder of -7/x+1.

You can prove this by multiplying (x+1)(-5x+2) + -7.
-5x^2 -5x+2x+2-7.
Simplify: -5x^2-3x-5

Feel free to email me; since I can probably format it better there so you can see what I describe in words.

Good luck!

Answer 3

I also assume that you mean (2x^3 - 7x^2 - 3x - 5)/(x + 1) and have prepared an image which shows how this is done. It doesn't really matter if the polynomials I have chosen are what you intended, the procedure is the same. See the image at

http://img176.imageshack.us/img176/2070/polynomialdivisioneh7.png


In case you really did mean (x + 1)/(2x^3 - 7x^2 - 3x -5), with the higher order poynomial in the denominator, i have also prepared an image showing the start of how that is done.


http://img168.imageshack.us/img168/4053/polynomialdivision2tf5.png

I hope this helps.

Answer 4

This denominator can be rewritten as -5x^2 - 3x -5.
Unless there is a typo in your problem, this denominator is an imaginary number. If you use the quadratic equation to solve for x, you will end up with the square root of a negative number
(-91) for part of the quadratic equation (sqrt(b^2 - 4ac)).
I assume there is an error

Answer 5

for what application does this have in the real world?

Answer 6

i wish I had this when i was in school. sheez