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algebra

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Use the rational zero theorem to list all possible rational zeros for the given function
f(x)=x^3-4x^2-19x-14

  • algebra -

    -2, -1, 7

  • algebra -

    try x = ±1, ±2, and ± 7
    f(1) = 1 - 4 - 19 - 14 ≠ 0
    f(-1) = -1 - 4 + 19 - 14 = 0
    ahhh, so (x+1) is a factor

    using algebraic division
    x^3-4x^2-19x-14 = 0
    (x+1)(x+2)(x-7) = 0
    so x = -1, -2 or 7

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