#x^2 + x + 2# is not factorable using rational numbers. This means that no rational numbers added together equal #1# (#x# in equation) and multiplied together equal #2#.

You can find the imaginary answer to #x^2 + x + 2 = 0# (an equation, notice the #=#), however.

Using the quadratic formula: #(-b+-sqrt(b^2-4ac))/(2a)#

#x# would then equal #(-1 +- isqrt(7))/2#

and the factors would be #x^2+x+2 = (x+(1+sqrt(7)i)/2)(x+(1-sqrt(7)i)/2)#