SOLUTION: solve inequality and write answer in interval notation 3x^5+6x^4-24x^2-48x<0

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Question 544733: solve inequality and write answer in interval notation
3x^5+6x^4-24x^2-48x<0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E5%2B6x%5E4-24x%5E2-48x%3C0
3x%5E4%28x%2B2%29-24x%28x%2B2%29%3C0
%28x%2B2%29%283x%5E4-24x%29%3C0
3x%28x%2B2%29%28x%5E3-8%29%3C0
You have 3 factors. Each becomes zero and changes from negative to positive exactly once, at a certain value of x. The zeros are at x=-2, x=0, and x=2.
For x>2, all 3 factors and the product are positive. As each factor changes sign, the product will be negative between 0 and 2, positive between -2 and 0, and negative for x<-2.
So I'd say (-infinity, -2) U (0,2).