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 August 5th, 2010, 05:30 AM #1 Newbie   Joined: May 2010 Posts: 19 Thanks: 0 factorize $\begin{array}{l} \text{factorize} \\ \\ (x + 1)(x + 2)(x + 3)(x + 4) + 1 \\ \end{array}$
August 5th, 2010, 05:52 AM   #2
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Re: factorize

Quote:
 Originally Posted by salamatr25 $\begin{array}{l} \text{factorize} \\ \\ (x + 1)(x + 2)(x + 3)(x + 4) + 1 \\ \end{array}$
(x+1(x+4)(x+2)(x+3)+1=(x²+5x+5-1)(x²+5x+5+1)+1=...

 August 5th, 2010, 05:55 AM #3 Senior Member   Joined: Sep 2008 Posts: 116 Thanks: 0 Re: factorize I think what SafeX is trying to say is: Try posting what you have tried and how far you have gotten. We're here to help, not to do problems for you.
 August 5th, 2010, 05:57 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1140 Math Focus: Elementary mathematics and beyond Re: factorize It's a perfect square (quadratic)^2. Expand it and notice that the coefficients of the x^3, x^2 and x terms are multiples of five and the constant term is a multiple of five.
August 5th, 2010, 06:10 AM   #5
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Quote:
 Originally Posted by SafeX (x+1(x+4)(x+2)(x+3)+1=(x²+5x+5-1)(x²+5x+5+1)+1=...
Let u = x² + 5x + 5. (u - 1)(u + 1) + 1 = u² - 1² + 1 = u² - 1 + 1 = u² = (u)(u). ? (x + 1)(x + 2)(x + 3)(x + 4) + 1 = (x² + 5x + 5)(x² + 5x + 5).

 August 5th, 2010, 06:13 AM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1140 Math Focus: Elementary mathematics and beyond Re: factorize
 August 5th, 2010, 06:29 AM #7 Senior Member   Joined: Apr 2010 Posts: 105 Thanks: 0 Re: factorize And what has salamantr25 to do?
 August 5th, 2010, 06:38 AM #8 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1140 Math Focus: Elementary mathematics and beyond Re: factorize He could study what is given and try to apply what he learns to similar problems.
August 5th, 2010, 07:20 AM   #9
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Re: factorize

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 Originally Posted by shynthriir I think what SafeX is trying to say is: Try posting what you have tried and how far you have gotten. We're here to help, not to do problems for you.
you do not do problems for me, just to see several solutions for this problem,

and you are not here to say what others try to say.

August 5th, 2010, 08:25 AM   #10
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Re: factorize

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 Originally Posted by salamatr25 you do not do problems for me, just to see several solutions for this problem, and you are not here to say what others try to say.
Gettin feisty in here!

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