My Math Forum Challenging Factoring Problem

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 November 8th, 2007, 06:38 PM #1 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Challenging Factoring Problem I spent about 20 minutes on this one. This one is probably the hardest factoring problem I solved in my mathematical education. I am posting this one for you guys to solve. Factor (1-2x-x^2)(1-2x+3x^2) + 4x^4. Show your work. Good luck! J.
 November 8th, 2007, 11:00 PM #2 Joined: Oct 2007 From: France Posts: 121 Thanks: 0 (1-2x-x^2)(1-2x+3x^2) + 4x^4 =(1-2x+xÂ²-2xÂ²)(1-2x+xÂ²+2xÂ²)+4x^4 =[(x-1)Â²-2x^Â²][(x-1)Â²+2xÂ²]+4x^4 =(x-1)^4-(2xÂ²)Â²+4x^4 =(x-1)^4
 November 9th, 2007, 04:16 PM #3 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Good job.
 October 6th, 2015, 03:45 AM #4 Newbie   Joined: Oct 2015 From: quebec Posts: 1 Thanks: 0 hard factoring question does anyone know how to solve this problem x4+7x2+64
 October 6th, 2015, 07:27 AM #5 Global Moderator   Joined: Dec 2006 Posts: 12,901 Thanks: 642 \displaystyle \begin{align*}(1-2x-x^2)(1-2x+3x^2) + 4x^4 &= (1 - 2x)^2 + 2x^2(1 - 2x) - 3x^4 + 4x^4 \\ &= 1 - 4x + 6x^2 - 4x^3 + x^4 \\ &= (1 - x)^4\end{align*} $\displaystyle x^4 + 7x^2 + 64 = (x^2 + 8 )^2 - 9x^2 = (x^2 - 3x + 8 )(x^2 + 3x + 8 )$

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