Help with polynomials

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I know a 5th degree polynomial is like ax^5 + ax^4 + ax^3 + ax^2 + ax + c
Right, and where does a polynomial have a root? When it crosses the 'x-axis' right?

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Well "real root" anyways
it is negative then positive then negative then positive
has a root in between each change in sign any polynomial is continuous, can't skip numbers
^Indeed In order to have a real root, we just see how many times the values alternate from - to +
Or + to - of course
So in the table it only flips two time s
Are you sure? Just 2?
well with the numbers given to us at least for p(x)
Well we start at -30 and go to 22....so thats 1 root and we go from 34 to -130 ....make that 2 roots And finally we go from that -130 to 222...so I count 3 roots
wows I didnt think of that i was just seeing 2 switches. but didnt think of the change after
So just to make sure I understand this, Say we have x=1,2,3,4,5,6 p(x)= -55, 100, 200, -225, 300, -325 So this would have; -55 to 100, 1 root 200 to -225, 2 roots -225 to 300, 3 roots 300 to -325, 4 roots ?
I would say that is correct!
Alright, sorry just reviewing some things for my Clep test. I take it on Friday D:
Been reviewing like Algebra 2 concepts for the past like month and a half trying to get everything settled out
No problem! And I understand...had to take a clep for english...felt like I was back in 5th grade lol
lool Welp Im taking the College algebra one S: Kinda scared cause like some of these things I am not getting

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