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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 (12xx^2)(12x+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 
(12xx^2)(12x+3x^2) + 4x^4 =(12x+xÂ²2xÂ²)(12x+xÂ²+2xÂ²)+4x^4 =[(x1)Â²2x^Â²][(x1)Â²+2xÂ²]+4x^4 =(x1)^4(2xÂ²)Â²+4x^4 =(x1)^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 
$\displaystyle \begin{align*}(12xx^2)(12x+3x^2) + 4x^4 &= (1  2x)^2 + 2x^2(1  2x)  3x^4 + 4x^4 \\ &= 1  4x + 6x^2  4x^3 + x^4 \\ &= (1  x)^4\end{align*}$ $\displaystyle x^4 + 7x^2 + 64 = (x^2 + 8 )^2  9x^2 = (x^2  3x + 8 )(x^2 + 3x + 8 )$ 

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