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Solve the polynomial inequality

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Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x^3+x^2+4x+4<0
The solution set is=

  • Solve the polynomial inequality -

    x^3+x^2+4x+4<0
    (x^2(x+1) + 4(x+1) < 0
    (x+1)(x^2+4) < 0

    well, x^2 + 4 is always positive, so the only way the whole thing < 0 if
    x+1 < 0

    x < -1

    check:
    good ol' Wolfram webpage
    http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3%2Bx%5E2%2B4x%2B4

    notice where the curve is below the x-axis ?

  • Solve the polynomial inequality -

    Thank you!!!

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