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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 
Senior Member Joined: Oct 2007 From: France Posts: 121 Thanks: 1 
(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: 14,778 Thanks: 890 
$\displaystyle \begin{align*}(12xx^2)(12x+3x^2) + 4x^4 &= (1  2x)^2 + 2x^2(1  2x)  3x^4 + 4x^4 \\ &= 1  4x + 6x^2  4x^3 + x^4 \\ &= (1  x)^4\end{align*}$ $\displaystyle x^4 + 7x^2 + 64 = (x^2 + 8 )^2  9x^2 = (x^2  3x + 8 )(x^2 + 3x + 8 )$ 
November 29th, 2015, 02:56 PM  #6 
Newbie Joined: Nov 2015 From: idk Posts: 1 Thanks: 0  Ummmmmmm I got the answer
It took me 3 minutes to answer that question and I'm a middle schooler < LOLOLOL The answer is (x1)^2(x^26x+1) (12xx^2)(12x+3x^2)+4x^4 = x^44x^3+6x^24x+1 = x^42x^2+14x^3+8x^24x = (x^21)^24x(x1)^2 = (x+1)^2(x1)^24x(x1)^2 =(x^26x+1)(x1)^2 You are welcome peoples. Last edited by skipjack; November 29th, 2015 at 03:26 PM. Reason: HAHA IM SMARTER THAN U 
November 29th, 2015, 03:25 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 14,778 Thanks: 890 
In your last line of working, you should have had (x^2  2x + 1)(x  1)^2, which is (x  1)^4.

November 29th, 2015, 03:58 PM  #8  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,181 Thanks: 405 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
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November 29th, 2015, 04:16 PM  #9 
Math Team Joined: Jul 2011 From: Texas Posts: 1,498 Thanks: 608  
November 30th, 2015, 12:32 PM  #10 
Senior Member Joined: Jun 2014 From: Earth Posts: 589 Thanks: 141  

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