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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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From: Lexington, MA

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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 $x^2 + x - 2 = (x + 2)(x - 1)$.

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