SOLUTION: what are the possible rational zeros and real zeros of f(x)=x^3+3x^2-2x-8

Question 621345: what are the possible rational zeros and real zeros of f(x)=x^3+3x^2-2x-8
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what are the possible rational zeros and real zeros of f(x)=x^3+3x^2-2x-8
**
Using the rational roots theorem:
...0..|.....1........3.......-2.......-8.........
...1..|.....1........4........2........-6 (There is an irrational root between 1 and 2) (change in sign of last number
...2..|.....1........5........8.........8 (2 is upper bound) (numbers>0)
==================
...0..|.....1........3.......-2........-8
.-1..|.....1........2.......-4........-4
.-2..|.....1........1.......-4.........0 (-2 is a root)
==================
...0..|.....1........1........-4
.-1..|.....1........0........-4
.-2..|.....1......-1........-2 (There is an irrational root between -2 and-3) (change in sign of last number
.-3..|.....1......-2..........2 (-3 is lower bound) (numbers alternate in sign)

f(x)=(x^2+x-4)(x+2)
one real rational zero and 2 irrational zeros

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