Find all roots of the polynomial equation f(x)= x^3+x+10 (study guide practice question)?

by integral root theorem, possible roots are +/-[1,2,5, and 10] ... test each
x = -2 is a root ... so (x + 2) is a factor ... divide (x^3 + x + 10)/(x + 2)
... this gives a quadratic .... use the quadratic formula
x = 1 +/- 2i

.... x = -2, x = 1 + 2i, and x = 1 - 2i