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August 5th, 2014, 02:33 PM   #1
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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.
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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:
$\quad \big([x^2+x+1] - 3\big)\big([x^2+x+1]+4\big) \;=\;(x^2 + x - 2)(x^2+x+5)$
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August 5th, 2014, 08:44 PM   #3
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Then use $x^2 + x - 2 = (x + 2)(x - 1)$.
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