## anonymous one year ago The value -2 is a lower bound for the zeros of the function shown below. f(x)=4x^3-12x^2-x+15

1. anonymous

True or false?

2. UsukiDoll

all positive values are upper bound all negative values are lower bound

3. anonymous

is it false? I use synthetic division right? I got 4, -20, 39, 171

4. UsukiDoll

can you draw that synthetic division for me?

5. anonymous

|dw:1437277905106:dw| sorry it's kind of hard to read but i just realized i messed up earlier haha is it still false though?

6. anonymous

because not everything is negative??

7. anonymous

i don't get it :/

8. UsukiDoll

$f(x)=4x^3-12x^2-x+15$ is our function oh I see we use -2 for synthetic division

9. UsukiDoll

|dw:1437278252692:dw|

10. UsukiDoll

so the first entry should go down |dw:1437278300525:dw|

11. UsukiDoll

then we multiply -2 x 4

12. UsukiDoll

|dw:1437278367948:dw| then use addition we should get -20

13. UsukiDoll

now -2 x -20 = 40 |dw:1437278417562:dw| and then we should have 39

14. UsukiDoll

|dw:1437278454846:dw|

15. anonymous

yup thats what i got too!

16. UsukiDoll

so now we can re-write this the last part should be $\frac{-63}{x-2}$ because -63 is the remainder

17. UsukiDoll

ok I'm going backwards in writing this since it's been a while

18. UsukiDoll

ack wrong sign $4x^2 -20x+39-\frac{63}{x+2}$

19. anonymous

so would it be true or false?

20. UsukiDoll

since -2 < 0 and the signs during the synthesis division alternate, we have a lower bound for real roots of the function.

21. anonymous

ohh. i get it, thank you :)

22. UsukiDoll

geez what is with my writing? I meant signs during the synthetic division alternate XD