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

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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?

3. madelyn97

yep! thanks!

4. satellite73

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

5. madelyn97

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

|dw:1353208613053:dw|

8. madelyn97

|dw:1353208683477:dw|

9. madelyn97

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

|dw:1353216271826:dw|

16. madelyn97

okay thanks!

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