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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 Senior Member   Joined: Oct 2007 From: France Posts: 121 Thanks: 1 (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 Thanks from junglemath
 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*}(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*} $\displaystyle x^4 + 7x^2 + 64 = (x^2 + 8 )^2 - 9x^2 = (x^2 - 3x + 8 )(x^2 + 3x + 8 )$ Thanks from junglemath
 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 (x-1)^2(x^2-6x+1) (1-2x-x^2)(1-2x+3x^2)+4x^4 = x^4-4x^3+6x^2-4x+1 = x^4-2x^2+1-4x^3+8x^2-4x = (x^2-1)^2-4x(x-1)^2 = (x+1)^2(x-1)^2-4x(x-1)^2 =(x^2-6x+1)(x-1)^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. Thanks from topsquark
November 29th, 2015, 03:58 PM   #8
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Quote:
 Originally Posted by SmartiePants It took me 3 minutes to answer that question and I'm a middle schooler <---- LOLOLOL The answer is (x-1)^2(x^2-6x+1) (1-2x-x^2)(1-2x+3x^2)+4x^4 = x^4-4x^3+6x^2-4x+1 = x^4-2x^2+1-4x^3+8x^2-4x = (x^2-1)^2-4x(x-1)^2 = (x+1)^2(x-1)^2-4x(x-1)^2 =(x^2-6x+1)(x-1)^2 You are welcome peoples.
Quote:
 Originally Posted by skipjack In your last line of working, you should have had (x^2 - 2x + 1)(x - 1)^2, which is (x - 1)^4.
It never pays to rush through the Math...

-Dan

November 29th, 2015, 04:16 PM   #9
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Quote:
 Originally Posted by Tom342 does anyone know how to solve this problem x4+7x2+64
Solve?

You can factor the expression ...

$x^4+7x^2+9x^2+64-9x^2$

$x^4+16x^2+64-9x^2$

$(x^2+8 )^2-9x^2$

$[(x^2+8 )-3x][(x^2+8 )+3x]$

$(x^2-3x+8 )(x^2+3x+8 )$

Only equations can be solved.

November 30th, 2015, 12:32 PM   #10
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Joined: Jun 2014
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Quote:
 Originally Posted by Tom342 does anyone know how to solve this problem x4+7x2+64
Tom342,

please start a new thread for a different problem. Thank you.

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