Trouble with Limits

Main Question or Discussion Point

(X^4-15X^3+32X+372X-1440)/X^2-X-30 as X approaches 6

I know that somehow I am supposed to be able to factor this, but I'm having trouble doing so, and am stuck with a TI-82 that isn't very much help, either. Could someone please show me how to do this by hand?
 

Answers and Replies

marcusl
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EDIT: Sorry, I was blind to the answer. mathwonk has it right in the next post...
 
Last edited:
mathwonk
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the root factor theorem says that if x=6 makes a polynomial zero, then x-6 is a factor, and vice versa.
 
(X^4-15X^3+32X+372X-1440)/X^2-X-30 as X approaches 6
did you write the question correctly?
is the third term in the numerator [itex]32x^2[/itex]?
then it becomes
[tex]\frac{x^4-15x^3+32x^2+372x-1440}{x^2-x-30}=\frac{(x+5)(x-8)(x-6)^2}{(x+5)(x-6)}=(x-8)(x-6)[/tex]

and this approaches 0 as x approaches 6.
 
Gib Z
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I would have a feeling you assumption is correct, murshid. Nice work
 
Thank you so much for your help!! All of you! It is very much apprecitated!
 
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Since the trouble was originally that you got 0/0 by plugging 6 in directly, you could also have used L'Hopital's rule. Of course, it is conceptually more elementary to factor the polynomial, but it may actually be less work to do 1 derivative than to do the polynomial long division.

Just offering an alternative.

--Stuart Anderson
 

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