#1 - Simplify your life. Same solutions as this: 0 = x^3 - 3x^2 - 24x - 28
#2 - Rule of Signs: One Positive Real. Two or Zero Negative
#3 - Rational Roots: +/-1, +/-2, +/-4, +/-7, +/-14, +/-28
--------- 7 Works
#4 - Reduction: (x^3 - 3x^2 - 24x - 28)/(x - 7) = (x^2 + 4x + 4)
#5 - That is easily factored.