A very very hard college algebra problem

In summary, the conversation is about a difficult problem that the person has posted on a forum without receiving an answer. They have included all relevant information and their attempts at solving it. The problem involves finding a polynomial and expressing it in terms of other polynomials. The conversation also includes a discussion about the use of combinations and an arbitrary constant in solving the problem.
  • #1
nmego12345
21
0

Homework Statement


Note: I'm saying it's very very hard because I still couldn't solve it and I've posted it in stackexchange and no answer till now.

I'm posting here the problem statement, all variables and known data in addition to my solving attempts. Because I'm posting an image of my question and that it would be hard to separate my solving attempts from the problem statement etc.., but they are obvious in the image. I'm posting an image because I'm not familiar to the formatting here yet, and I don't have time to format all this problem again ( took me 1.5 hours to format)

https://s3.amazonaws.com/diigo/thum...][/B][/B] [h2]The Attempt at a Solution[/h2]
 
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  • #2
We need to state the problem correctly. Isn't the problem to find a polynomial ##f_k (x)## such that ##f_k(x)- f_k(x-1) = x^k## ?
 
  • #3
I'm not sure If I understand the problem correctly, I found it on a textbook, I didn't invent it, but I think
that you're correct
 
  • #4
Let ##p(x) = x^{k+1} + ...## other terms. Suppose, for example, that ##p(x) - p(x-1)## has the term ##Cx^3##.

By part 2) , if you form the new polynomial ## q(x) = p(x) - C f_3(x) ## then

##q(x) - q(x-1) = p(x) - p(x-1) + C (f_3(x) - f_3(x-1)) = x^{k+1}+ ... Cx^3 + ... - C x^3## so you can eliminate the ##Cx^3## term by subtracting a multiple of ##f_3(x)##.

I think what the problem wants you to do is express ##f_k(x)## as ##x^k## minus multiples of ##f_{k-1}, f_{k-2},...##.

After you do that, you may be able to find the numerical values of the coefficients, but perhaps the problem only wants you to write the "recursive" relation between ##f_k## and ##f_{k-1}, f_{k-2} ... ##.
 
  • #5
First of all, what is Cx3?, is it combinations? but combinations are defined over 2 numbers not 1 number. Is it an arbitary constant?
 
  • #6
nmego12345 said:
First of all, what is Cx3?, is it combinations? but combinations are defined over 2 numbers not 1 number. Is it an arbitary constant?

C is an arbitrary constant.
 
  • #7
nmego12345 said:
First of all, what is Cx3?, IIRC, aren't combinations have 2 numbers to begin with?

Oh Ok, I reread your answer, that makes sense.
 

Related to A very very hard college algebra problem

1. What is the difficulty level of the college algebra problem?

The difficulty level of a college algebra problem can vary depending on the individual's mathematical skills and knowledge. However, a "very very hard" problem would typically require a high level of understanding and proficiency in algebra.

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Some common mistakes to avoid when solving a difficult college algebra problem include forgetting to use the order of operations, not fully simplifying equations, and not checking for extraneous solutions. It is also important to double check your work and make sure you are following the given instructions correctly.

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