The rational root (or zero) theorem says a polynomial's rational zeros must have factors of the constant in the numerator and those of the leading coefficient in the denominator.
Here the leading coefficient is 1 and the constant is 5, so our only possibilities for rational roots are 1, -1, 5, -5
We try them each in term
1-3+1+5=6 nope
-1 -3 -1 +5 = 0 yes, x = -1 is a rational zero
5 and -5 don't work either so we're left with
Final answer: x = -1
