## madelyn97 2 years ago The function f(x)=x^3-5x^2-2x=24 is positive for what parts of its domain?

1. Freyes

Well in this situation the best thing to do would be to simplify it.. into factors. then you have ranges of test cases to test whether a number is positive in that range

2. Freyes

can you factor it?

yep! thanks!

4. satellite73

is it $f(x)=x^3-5x^2-2x+24$

yeah!

6. satellite73

did you factor? once you have the three zeros, because this is a third degree polynomial with positive leading coefficient you know it will be negative, then positive, then negative, then positive

7. satellite73

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but that doesnt work right?

10. Freyes

hmm i can factor this one out give me a second

11. Freyes

I think what you meant to do was $(x+2)(x-3)(x-4)$

12. Freyes

This gives you the ranges of $(-\infty, -2) : (-2,3) : (3,4) :( 4,\infty)$

13. Freyes

Then you can just plug a number from each of those ranges in between and just look at the sign.

14. Freyes

That'll tell you if it's in the positive range or not

15. cinar

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