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  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, alexstrasuz! Quote:
We have: $\:\big(x^2 + x + 1\big)\big([x^2+x+1] + 1\big) 12$ Let $u \,=\,x^2+x+1$ Substitute: $\:u(u+1) 12 \;=\;u^2 + u  12 \;=\; (u3)(u+4)$ Backsubstitute: $\quad \big([x^2+x+1]  3\big)\big([x^2+x+1]+4\big) \;=\;(x^2 + x  2)(x^2+x+5)$  
August 5th, 2014, 08:44 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
Then use $x^2 + x  2 = (x + 2)(x  1)$.


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