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 August 5th, 2014, 02:33 PM #1 Newbie   Joined: Aug 2014 From: Tesanj Posts: 2 Thanks: 0 Factors Separate this polynomial in factors (x^2+x+1)*(x^2+x+2)-12 Last edited by skipjack; August 5th, 2014 at 08:40 PM. August 5th, 2014, 04:47 PM   #2
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Hello, alexstrasuz!

Quote:
 Separate this polynomial in factors $\quad (x^2+x+1)(x^2+x+2)-12$

We have: $\:\big(x^2 + x + 1\big)\big([x^2+x+1] + 1\big) -12$

Let $u \,=\,x^2+x+1$

Substitute: $\:u(u+1) -12 \;=\;u^2 + u - 12 \;=\; (u-3)(u+4)$

Back-substitute:
$\quad \big([x^2+x+1] - 3\big)\big([x^2+x+1]+4\big) \;=\;(x^2 + x - 2)(x^2+x+5)$ August 5th, 2014, 08:44 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 Then use $x^2 + x - 2 = (x + 2)(x - 1)$. Tags factors Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post nukem4111 Number Theory 2 October 6th, 2013 08:08 AM mathbalarka Number Theory 15 June 15th, 2012 07:36 PM loaiello Number Theory 4 February 26th, 2011 08:24 AM naserellid Algebra 1 August 14th, 2010 07:22 AM Tartarus Algebra 7 December 11th, 2009 09:01 PM

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