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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

**Dividing Polynomials - Mix of Sums**

**1. (x[sup]3[/sup] + 2x[sup]2[/sup] - 120x) ÷ (x + 12)2. (-2x[sup]3[/sup] + 40x[sup]2[/sup] - 192x) ÷ (x - 8)3. (-2x[sup]4[/sup] + 14x[sup]3[/sup] + 162x[sup]2[/sup] - 1134x) ÷ (-2x)4. (51x[sup]4[/sup] - 204x[sup]3[/sup] + 4964x[sup]2[/sup] - 20400x - 13600) ÷ (17)5. (x[sup]3[/sup] - 4x[sup]2[/sup] - 25x + 100) ÷ (x - 4)6. (16x[sup]3[/sup] - 6x[sup]2[/sup] - 18x) ÷ (8x[sup]2[/sup] - 3x - 9)7. (x[sup]3[/sup] - 15x[sup]2[/sup] + 36x) ÷ (x - 12)8. (11x[sup]4[/sup] + 34x[sup]3[/sup] - 534x[sup]2[/sup] + 454x - 45) ÷ (x[sup]2[/sup] + 4x - 45)9. (x[sup]4[/sup] - 12x[sup]3[/sup] + 4x[sup]2[/sup] + 192x - 320) ÷ (x - 10)10. (-x[sup]3[/sup] + 12x[sup]2[/sup] - 46x + 60) ÷ (-x[sup]2[/sup] + 6x - 10)11. (x[sup]3[/sup] + 18x[sup]2[/sup] + 80x) ÷ (x + 10)12. (25x[sup]4[/sup] - 60x[sup]3[/sup] + 57x[sup]2[/sup] - 24x + 4) ÷ (-5x[sup]2[/sup] + 4x - 1)13. (4x[sup]4[/sup] - 48x[sup]2[/sup]) ÷ (4x)14. (x[sup]4[/sup] + 2x[sup]3[/sup] - 90x[sup]2[/sup] - 162x + 729) ÷ (x[sup]2[/sup] + 2x - 9)15. (-27x[sup]4[/sup] + 225x[sup]3[/sup] - 276x[sup]2[/sup] + 168x) ÷ (3x)16. (2x[sup]3[/sup] - 18x[sup]2[/sup] + 40x) ÷ (x - 5)17. (x[sup]4[/sup] + x[sup]3[/sup] - 33x[sup]2[/sup] - 3x + 90) ÷ (x[sup]2[/sup] + x - 30)18. (5x[sup]5[/sup] - 11x[sup]4[/sup] + 239x[sup]3[/sup] - 539x[sup]2[/sup] - 294x) ÷ (x)19. (-3x[sup]4[/sup] + 12x[sup]3[/sup] - 147x[sup]2[/sup] + 588x) ÷ (x - 4)20. (7x[sup]5[/sup] - x[sup]4[/sup] + 60x[sup]3[/sup] - 9x[sup]2[/sup] - 27x) ÷ (x)21. (-3x[sup]3[/sup] + 36x[sup]2[/sup] - 105x) ÷ (x[sup]2[/sup] - 12x + 35)22. (4x[sup]3[/sup] - 4x[sup]2[/sup] - 528x) ÷ (x - 12)23. (-3x[sup]5[/sup] + 327x[sup]3[/sup] - 2700x) ÷ (-3x)24. (0) ÷ (0)25. (x[sup]4[/sup] + x[sup]3[/sup] - 19x[sup]2[/sup] - 7x + 84) ÷ (x - 3)26. (-40x[sup]5[/sup] + 24x[sup]4[/sup] - 44x[sup]3[/sup] + 24x[sup]2[/sup] - 4x) ÷ (4x)27. (4x[sup]4[/sup] + x[sup]3[/sup] + 2x[sup]2[/sup] + x - 2) ÷ (4x[sup]2[/sup] + x - 2)28. (2x[sup]4[/sup] + 9x[sup]3[/sup] - 85x[sup]2[/sup] - 4x + 288) ÷ (x - 4)29. (2x[sup]3[/sup] + 2x[sup]2[/sup] - 12x) ÷ (x + 3)30. (9x[sup]4[/sup] + 144x[sup]2[/sup]) ÷ (-3x)**

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*Last edited by Devanté (2006-10-11 04:39:53)*

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**unique****Member**- Registered: 2006-10-04
- Posts: 419

we have to solve these?

Desi

Raat Key Rani !

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Yes.

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**unique****Member**- Registered: 2006-10-04
- Posts: 419

yes. oh god and there 30 problems..ok first let me try to do my problem then i'll come back to this

Desi

Raat Key Rani !

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

You don't have to solve all of them. Just do the ones you want to do.

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**unique****Member**- Registered: 2006-10-04
- Posts: 419

yeah ok lemme see......

but for me all will seem to be a bit hard..cause i really dont have practice in doing such problems

Desi

Raat Key Rani !

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

This exercise deals with dividing polynomials with monomials, trinomials, binomials, etc.

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**janusweet_pandit****Member**- Registered: 2007-08-15
- Posts: 0

i acn't do it i am only in grade 4th!!!!!!

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

lol 24

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**MAD****Member**- Registered: 2011-03-15
- Posts: 2

1.x^3 + 2x^2 - 120x = x^3 + 12x^2 - 10x^2 - 120x

= x^2(x +12) -10x(x + 12)

= (x + 12)(x^2 - 10x)

So, cancelling the terms (x - 12), we get x^2 - 10x.

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

Hint: All those where you are dividing by a binomial or a trinomial have remainder zero.

Dividing by a binomial yields remainder zero.

Dividing by a trinomial yields remainder 0x+0 = 0.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

0 / 0 is undefined.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

Hi stefy!

0/0 is indeed undefined. That's been mulled over pretty well on one of the threads, eh?

Devante rigged his divisions by binomials and trinomials all to have remainder zero.

That way gives somewhat of a check on whether one is obtaining a correct answer.

One can learn lots of math (a wide variety) by interacting on this site. And three

cheers for the internet, wikipedia, etc. that gives us almost instant access to lots of info.

There might not be anything left to discover if the biggies like Gauss, Fermat, Euclid, ...

had such communication possibilities.

You are doing fantastic for your age! Keep it up. My age? It is twixt twin primes and has

five prime factors.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

That was my answer to his question.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

That is only the answer to one of these. I am sure Devante knows that too.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Yes, I was just saying. I wasn't trying to repeat it.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hooba habba, hooba habba, hooba habba...

Sorry, that is my favorite song. I know you were just saying, I was just talking to you.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

That sounds like a song of some kind of jungle people.

Whatever. I just hope the dragon won't eat the hippo's ear.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

That is very good. A hippo is dangerous creature way too much for a dragon, now a draconian?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Oh, yeah. They are almost as dangerous as hippos, hopping from bubble to bubble.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

The bubble hoppers are something different. We call them by another name here. Her explanations are kaboobly doo.

A winged Draco comes from Draconis.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Okay, seems she has them mixed up a little.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

She is the enemy. You can not expect her to be entirely open.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

It is possible to generalize synthetic division to handle any of these divisions by binomials or larger. It only involves three steps repeated over and over until the remainder is finished. That makes these divisions much easier and about 10 times faster since you don't have to write the powers of x.

In fact these divisions can be done by the "usual method" (repeated subtraction algorithm) much faster if one just writes the coefficients of the powers of x. After all polynomials are a place value system just like base 10 arithmetic. The main difference is that it is place value in an unknown base x. As such one cannot carry or borrow. This makes the arithmetic of polynomials easier than base 10 arithmetic. And it is not just division that can be done easier in this short form.

Adding, subtracting, multiplying and factoring can be done easier also.

Hi bobbym!

My signature still doesn't show up, does it? Am I doing something wrong that it won't work?

Where would a thread concerning "the language of mathematics" fit in? Would we have to

create a new thread to deal with this?

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,247

Hi noelevans;

I can see your signature but you have not been a member long enough for it to appear. You signed up 7 / 20 / 2012 which is not quite the grace period yet. Have patience it will appear.

Where would a thread concerning "the language of mathematics" fit in? Would we have to

create a new thread to deal with this?

I am glad you asked that question before you went and did it.

Discussions like that can easily get out of hand. I have already had step in on another thread to stop the bickering.

People who feel that mathematics is a little funky always get the sternest resistance. People will come in from other forums to attack them. Pretty soon there is bad blood and I am forced to act like Mussolini.

I have been on both sides in those arguments and have seen the mayhem they cause on other forums.

That is just my experience and I am certainly not going to censure anyone based on what might happen. Start your thread in Members only or Dark discussions and good luck.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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