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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

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  • 1 decade ago
    Favorite 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

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