(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex](6x^4-3x^2+x-4) / (2x^2+1)[/tex]

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:

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

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

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

[tex](3x^2)(2x^2+1) = 6x^4+3x^2[/tex]

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

[tex](6x^4-3x^2) - (6x^4+3x^2) = -6x^2[/tex]

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

[tex]-6x^2-4[/tex]

Then I multiply the divisor by negative three and subtract the product from [tex]-6x^2-4[/tex]:

[tex](2x^2+1)(-3) = -6x^2-3[/tex]

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

-1 + x

So, my answer is [tex]3x^2-3+\frac{-1+x}{2x^2+1}[/tex]

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

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# Homework Help: Quick Help Dividing Polynomials

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