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How would i factor this Equation..?
I want to take the limit as x-->3 of
(x^4 - 18x^2 + 81) / (x-3)^2
so i want to factor so i don't get zero at the botton. Any help? thanks.
1 Answer
- Roger the MoleLv 71 decade agoFavorite Answer
Factor the numerator:
(x^4 - 18x^2 + 81)
Make the simplifying substitution y = x^2, y^2 = x^4:
y^2 - 18y + 81
Factor:
(y - 9)^2
Undo the substitution:
(x^2 - 9)^2
Factor what remains in parentheses:
((x + 3) (x - 3))^2
or
(x + 3)^2 (x - 3)^2
Put it all back into the original problem:
((x + 3)^2 (x - 3)^2) / (x-3)^2
Cancel the (x-3)^2 terms:
(x+3)^2
Continue with the limit evaluation:
(x+3)^2 lim x-->3 = 36