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November 8th, 2007, 06:38 PM   #1
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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.
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November 8th, 2007, 11:00 PM   #2
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(1-2x-x^2)(1-2x+3x^2) + 4x^4
=(1-2x+x²-2x²)(1-2x+x²+2x²)+4x^4
=[(x-1)²-2x^²][(x-1)²+2x²]+4x^4
=(x-1)^4-(2x²)²+4x^4
=(x-1)^4
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November 9th, 2007, 04:16 PM   #3
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Good job.
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October 6th, 2015, 03:45 AM   #4
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hard factoring question

does anyone know how to solve this problem
x4+7x2+64
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October 6th, 2015, 07:27 AM   #5
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$\displaystyle \begin{align*}(1-2x-x^2)(1-2x+3x^2) + 4x^4 &= (1 - 2x)^2 + 2x^2(1 - 2x) - 3x^4 + 4x^4 \\
&= 1 - 4x + 6x^2 - 4x^3 + x^4 \\
&= (1 - x)^4\end{align*}$

$\displaystyle x^4 + 7x^2 + 64 = (x^2 + 8 )^2 - 9x^2 = (x^2 - 3x + 8 )(x^2 + 3x + 8 )$
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November 29th, 2015, 02:56 PM   #6
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Talking 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
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November 29th, 2015, 03:25 PM   #7
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In your last line of working, you should have had (x^2 - 2x + 1)(x - 1)^2, which is (x - 1)^4.
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November 29th, 2015, 03:58 PM   #8
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Quote:
Originally Posted by SmartiePants View Post
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 View Post
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
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November 29th, 2015, 04:16 PM   #9
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Quote:
Originally Posted by Tom342 View Post
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.
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November 30th, 2015, 12:32 PM   #10
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Quote:
Originally Posted by Tom342 View Post
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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