Since it is impossible to find rational factors for the expression, the expression is "prime".
If irrational factors are needed, the quadratic formula can be used:
x=(-10 +/- sqrt(10^2+72))/2=-5 +/- sqrt(43)
hence the irrational factors are
x^2+10x-18 = (x+5+sqrt(43)) (x+5-sqrt(43))
