Homework Help: Quick Help Dividing Polynomials

1. Oct 14, 2007

marcflores

1. The problem statement, all variables and given/known data

$$(6x^4-3x^2+x-4) / (2x^2+1)$$

2. Relevant equations

Relevant equations???

3. The attempt at a solution

Here is my attempt, but I want to make sure that I didn't break any laws by changing the number to be divided by switching the last two terms around by using the commutative law of addition:

$$[6x^4-3x^2+(-4)+x]$$ -- is this okay so far?

So, I wrote $$2x^2+1$$ divided by $$[6x^4-3x^2+(-4)+x]$$

Then I wrote it out like long division (can't find the division symbol in laTex) and here are the steps I took:

$$(3x^2)(2x^2+1) = 6x^4+3x^2$$

Then, I subtracted the product from the first two terms of the dividend:

$$(6x^4-3x^2) - (6x^4+3x^2) = -6x^2$$

Carry down the +(-4) from the dividend and I have:

$$-6x^2-4$$

Then I multiply the divisor by negative three and subtract the product from $$-6x^2-4$$:

$$(2x^2+1)(-3) = -6x^2-3$$

That leaves me with -1 and I carry down the x from the dividend leaving:

-1 + x

So, my answer is $$3x^2-3+\frac{-1+x}{2x^2+1}$$

I just want to know if this is correct or if I was wrong in redistributing the terms in the original dividend. Thanks.

2. Oct 14, 2007

marcflores

Jeez, re-reading my post even left me confused. It's too bad I can't replicate it on the forums as I have it written on my paper.

3. Oct 14, 2007