SOLUTION: PlEASE help with polynomial long division.I've tried a million times and just cant get it. :/ (x^3+2x^2+3x-6)/(x-1) and (n^3-27)/(n-3) PlEASE show steps also =) Thanks in advance.

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Question 288025: PlEASE help with polynomial long division.I've tried a million times and just cant get it. :/ (x^3+2x^2+3x-6)/(x-1) and (n^3-27)/(n-3) PlEASE show steps also =) Thanks in advance.
Found 2 solutions by vleith, Theo:
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
Use this URL. It shows all the steps
http://www.calc101.com/webMathematica/long-divide.jsp

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Polynomial division is not much different than regular long division.
Here's how you do it step by step.

Your dividend is the expression you want to divide into.

It is

Your divisor is the expression you want to divide into the dividend.

It is

You set up your equation as shown in step 1 of the following picture.

In step 1 you are dividing by to get .

You subtract that from to get a remainder of .

You bring down the from the original dividend as shown in step 1 to make the remainder equal to as shown in step 2.

You divide of that remainder by to get which you place above the original dividend as shown in step 1.

You multiply times to get which you subtract from as shown in step 2.

You get a remainder of .

You bring down the from the original dividend as shown in step 1 to get a remainder of as shown in step 3.

You divide into as shown in step 2 to get which you place above of the original dividend as shown in step 1.

You multiply times 6 to get which you subtract from to get a remainder of 0 as shown in step 4.

You stop at step 4 because you have nothing left to divide into.

Your answer is with zero remainder.

To confirm that it's good, you multiply it by to get the original dividend.

That happens in steps 5 and 6 with the result shown in step 7.

Since you are able to get the same dividend that you started with, your division is good.

The result of your division is as shown in step 1.

Your original dividend is as shown in step and confirmed in step 7.

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You are always dividing the highest order of the divider into the highest order of the remainder of the dividend.

You are then always multiplying the whole divisor by the result of that division.

You are then subtracting the result of that multiplication from the remainder.

Once you get your remainder from the division, you are always bringing down the next lower order term from the original dividend.

Follow the steps through and you'll see how it was done.

Now we'll go on to your next problem.

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That problem worked out by hand is shown below:

With this problem, you are dividing by .

Since you are missing lower order exponents in the dividend, you need to fill them in.

That will make further processing easier.

is equal to after you fill in the missing lower order exponent terms.

Now you are ready to begin.

You are always dividing the highest order of the divisor into the highest order of the remainder of the dividend.

When you start the division, the remainder of the dividend is the dividend itself.

You Divide into as shown in step 1.

You get which you place above the as shown in step 1.

You multiply times to get which you subtract from as shown in step 1.

You get a remainder of and bring down from the original dividend to get a remainder of as shown in step 2.

You divide by to get which you place above as shown in step 1.

You multiply times to get which you subtract from as shown in step 2.

You get a remainder of .

You bring down the from the original dividend as shown in step 1.

You get a remainder of as shown in step 3.

You divide by to get 9.

You place that above the as shown in step 1.

You multiply by to get .

You subtract from as shown in step 3 to get a remainder of 0 as shown in step 4.

Since there is nothing left to divide, you are done.

You then confirm the answer is correct by multiplying as shown in step 1 by to see if you can get back to the original dividend.

That's done in steps 5 and 6 with the result shown in step 7.

Since you get the original dividend, the division is good.

The result of the division is as shown in step 1.

The original dividend is as shown above step 1 and confirmed in step 7.