How do you factor #x^2 + x + 1 ?

1 Answer
Alan P.
May 4, 2015

To factor x^2+x+1x2+x+1
use the quadratic formula for roots
x=(-b+-sqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a

In this case:
x= (-1+-sqrt(1^2-4(1)(1)))/(2(1))x=−1±√12−4(1)(1)2(1)

x = -1/2 +-sqrt(-3)/2x=−12±√−32

With no Real roots
and thus no factors if we are restricted to Real numbers.

However, if we are allowed to venture into Complex numbers
x= -1/2 +-sqrt(3)/2ix=−12±√32i

and the factors are
(x+1/2+sqrt(3)/2i)(x+1/2-sqrt(3)/2)(x+12+√32i)(x+12−√32)

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