Is the value -1 a lower bound for the zeros of the function f(x)=x^4+x^3-11x^2-9x+18 ?

Question

anonymous · Answer

@ranga for this problem I got 1,0,-11,2,16. would this be true since there are both negative and positive outcomes? I'm not too sure how lower bounds work

anonymous · Answer

alternates, (assuming you are right) then the answer is "yes" it is a lower bound

ranga · Answer

You do a synthetic division and if the coefficients of the quotient and remainders alternate in sign then it will be a lower bound.

anonymous · Answer

oh wait, it does not alternate, sorry i didn't look closely

anonymous · Answer

thank you! i did synthetic division and those are the numbers I got so I hope they are correct! I just learned how to do synthetic division today so I'm not very confident in it

anonymous · Answer

did i do my math incorrectly?

ranga · Answer

let me check.

anonymous · Answer

this polynomial has been cooked up
it actually factors completely over the integers (i.e. you can factor it)

ranga · Answer

Yes. You are correct.  It does not alternate so it is false.

anonymous · Answer

thank you both so much!! :)

ranga · Answer

you are welcome.