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

1 Answer
May 4, 2015

To factor #x^2+x+1#
use the quadratic formula for roots
#x=(-b+-sqrt(b^2-4ac))/(2a)#

In this case:
#x= (-1+-sqrt(1^2-4(1)(1)))/(2(1))#

#x = -1/2 +-sqrt(-3)/2#

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)/2i#

and the factors are
#(x+1/2+sqrt(3)/2i)(x+1/2-sqrt(3)/2)#