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Use factorization to simplify the given expression in part (a). Then find the indicated limit in part (b).
(a)
3x3 + 9x2 + 9x + 3
x4 + x3 + x + 1



(b)
lim
x → −1
3x3 + 9x2 + 9x + 1
x4 + x3 + x + 1

  • Math -

    did you mean
    3x^3 + 9x^2 + 9x + 3 ? If so, then
    = 3(x+1)(x+1)(x+1)

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

    so in your limit you would have

    lim 3(x+1)^3 / ((x+1)^2(x^2 - x + 1) as x=-1
    = lim 3(x+1)/(x^2 - x + 1)
    = 0/3 = 0

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