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March 7th, 2010, 09:46 AM   #1
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P / Q polynomials and zeros

Having trouble with this problem. i'm able to find one of the zeros, but the books answer lists two more and i do not understand how they got them.

F(x)= 4x^5 - 8x^4 -x +2

for P (just assume all of these are plus/minus): 1,2
Q: 1, 2, 4

p/q: 1/2, 1/4


since the polynomial goes from 5 to 4 to 1, i set up synthetic division using the value of 2 like this
2| 4 -8 0 0 -1 2
_| 8 0 0 0 -2
_____________________
4 0 0 0 -1| 0


so positive 2 gave me a zero. i am not sure where to go from here, or how to the bottom part of that synthetic to set up something that i could factor or use the quadratic formula on.
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March 7th, 2010, 10:01 AM   #2
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Re: P / Q polynomials and zeros

is the remaining polynomial 4x^4 - 1 ??
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March 7th, 2010, 10:38 AM   #3
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Re: P / Q polynomials and zeros

Yes.
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March 7th, 2010, 11:02 AM   #4
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Re: P / Q polynomials and zeros

come on greg help me out here, haha


so if i set that = to zero


4x^4 - 1 = -

4x^4 = 1

x^4 = 1/4


what do i do from there?
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March 7th, 2010, 11:07 AM   #5
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Re: P / Q polynomials and zeros

i need to somehow arrive at plus or minus sqr. rt 2 / 2 for the other two
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March 7th, 2010, 11:24 AM   #6
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Re: P / Q polynomials and zeros

4x^4 - 1 = (2x^2 - 1)(2x^2 + 1)
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March 7th, 2010, 11:30 AM   #7
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Re: P / Q polynomials and zeros

ooooh! wow thank you so much... can i ask how you knew to factor that instead of just setting it equal to zero so i can spot that in future problems?
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March 7th, 2010, 11:32 AM   #8
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Re: P / Q polynomials and zeros

I recognized it as a difference of squares.
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March 7th, 2010, 12:20 PM   #9
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Re: P / Q polynomials and zeros

flying through these problems now, thanks

i owe you a brand new car
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