Master Long Division: Get Help After 5 Years of Not Using It

[maverick99]

It's been at least 5 years since I've used long division. I managed to do the first half but I have no clue on how to finish it. I will appreciate any kind of help.

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[robert Ihnot]

You are doing the problem wrong since the leading term after division is 3x^2, this comes about since (2x-1)(3x^2) = 2x^2---. Your leading term of -8x^2, will not work.

 

[maverick99]

alright sounds good

 

[Jeff Lawson]

Don't read the attached file unless you want the answer!

It's a few decades since I thought about things like this but I do remember being unhappy with such problems!

The solution I provided follows a trial and error method whereby you have to make intelligent guesses to arrive at the right answer, i.e. to 'figure it out'! I was reasonably good at doing this but I always thought it was not a good method because I there must be some equations for which I would never be able to work through all the right combinations of possible factors. Just imagine having decimals in such equations!

Well. maths teachers while being very good at getting people through exams, generally avoid dealing with 'real world' problems...the sort that I always knew were out there and that I wouldn't be able to solve by trial and error. Luckily, the people who write exam questions are in on this conspiracy so they make sure that 'everything works out okay'! That's why I was able to guess that the denominator was probably a factor of the numerator.

In the real world: spend a few minutes trying to figure out a solution and if you don't look like getting any where then use the cubic equation formula that I supplied as a link in the attached file.

Similar formulae exist for quartic and quintic equations but, as I recall, not for higher powers.

 

[Edward Powell]

Hi

For long division involving polynomials, you need a format similar to that of normal long division not involving polynomials.


3x^2-4x+5
i.e. 2x-1 )6x^3-11x^2+14x-5
subt 6x^3-3x^2
-8x^2 +14x
subt -8x^2 + 4x
10x-5
subt 10x-5
0

i.e 6x^3 divided by 2x = 3x^2
3x^2 multiply 2x = 6x^3
3x^3 mulptiply -1 = -3x^x

subt. 6x^3 from 6x^3=nothing
subt. -3x^2 from -11x^2=-8x^2, then you bring down the 14x inline and start the process all over again.


Ans. = 3x^2-4x+5

 

[maverick99]

Sweet! Thx for the help guys!

 

[Jeff Lawson]

Sorry! I made a mistake while copying and pasting plus and minus symbols!

The attached version has been corrected for typos!

 

[DivineNathicana]

There's no way to factor that further, right? Like 3x^2-4x+5=x^2-4x=15 and nothing adds up to -4 and multiplies out to 15, does it? I hate when that happens haha I feel incomplete. *tear*

- Alisa