Trouble with Limits

(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?

marcusl
Gold Member
EDIT: Sorry, I was blind to the answer. mathwonk has it right in the next post...

Last edited:
mathwonk
Homework Helper
2020 Award
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 $32x^2$?
then it becomes
$$\frac{x^4-15x^3+32x^2+372x-1440}{x^2-x-30}=\frac{(x+5)(x-8)(x-6)^2}{(x+5)(x-6)}=(x-8)(x-6)$$

and this approaches 0 as x approaches 6.

Gib Z
Homework Helper
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!

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