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

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

Mathematics
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True or false?
all positive values are upper bound all negative values are lower bound
is it false? I use synthetic division right? I got 4, -20, 39, 171

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can you draw that synthetic division for me?
|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?
because not everything is negative??
i don't get it :/
\[f(x)=4x^3-12x^2-x+15 \] is our function oh I see we use -2 for synthetic division
|dw:1437278252692:dw|
so the first entry should go down |dw:1437278300525:dw|
then we multiply -2 x 4
|dw:1437278367948:dw| then use addition we should get -20
now -2 x -20 = 40 |dw:1437278417562:dw| and then we should have 39
|dw:1437278454846:dw|
yup thats what i got too!
so now we can re-write this the last part should be \[\frac{-63}{x-2} \] because -63 is the remainder
ok I'm going backwards in writing this since it's been a while
ack wrong sign \[4x^2 -20x+39-\frac{63}{x+2}\]
so would it be true or false?
since -2 < 0 and the signs during the synthesis division alternate, we have a lower bound for real roots of the function.
ohh. i get it, thank you :)
geez what is with my writing? I meant signs during the synthetic division alternate XD

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