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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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