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solve the polynomial inequalityx^3 + x^2 + 9x +9 <0

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2 Answers

In addition to John's work:
(x2 + 9) is always positive, thus we have to find solution for x + 1 < 0 ---> x < -1
Interval (-∞, -1) is the solution for given inequality.

Begin by separating the factors into two groups:

(x3 + x2) + (9x + 9) < 0

Factor out the GCF in each parenthesis

x2(x + 1) + 9(x + 1) <0

Since factor in parenthesis is the same, we can combine the GCF's into their own factor

(x2 + 9)(x + 1) < 0