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# Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as... (continued in desc.)

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Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity.

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If you could give me the answer to this question quickly, that would be very helpful. Thanks!

Jan 29, 2018

#2
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"Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity."

Jan 31, 2018

#1
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I think that there is something wrong with your question.

That division has a remainder .....

Jan 30, 2018
#2
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"Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity."

Alan Jan 31, 2018
#3
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But Alan

3(x^4+x^3+x^2+1)/(x^2+x-2)

does not divide to give a polynomial so how can you say that this question makes sense.  ?

Jan 31, 2018
#4
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The question doesn’t say that f(x) is a polynomial; it just asks for g(x) to be a polynomial, and for the limit of the sum of the two functions to have a zero asymptote.

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Alan  Jan 31, 2018
#5
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Well it doesn't make sense to me, it says that division gives a polynomial g(x)

"Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity."

Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2).

Find a polynomial g(x) such that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity.

Melody  Jan 31, 2018
edited by Melody  Jan 31, 2018
#6
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I don’t think it says division gives a polynomial Melody! There is a full stop (period) between the function definition and the word Give (which also starts with a capital letter), so I interpreted the sentence beginning with Give as an instruction to the reader, not a continuation of the previous sentence.

Alan  Feb 1, 2018