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March 7th, 2010, 09:46 AM  #1 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  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. 
March 7th, 2010, 10:01 AM  #2 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  Re: P / Q polynomials and zeros
is the remaining polynomial 4x^4  1 ??

March 7th, 2010, 10:38 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: P / Q polynomials and zeros
Yes.

March 7th, 2010, 11:02 AM  #4 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  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? 
March 7th, 2010, 11:07 AM  #5 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  Re: P / Q polynomials and zeros
i need to somehow arrive at plus or minus sqr. rt 2 / 2 for the other two

March 7th, 2010, 11:24 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: P / Q polynomials and zeros
4x^4  1 = (2x^2  1)(2x^2 + 1)

March 7th, 2010, 11:30 AM  #7 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  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?

March 7th, 2010, 11:32 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: P / Q polynomials and zeros
I recognized it as a difference of squares.

March 7th, 2010, 12:20 PM  #9 
Member Joined: Feb 2009 Posts: 52 Thanks: 0  Re: P / Q polynomials and zeros
flying through these problems now, thanks i owe you a brand new car 

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polynomials, zeros 
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