Question

what are the rational zeros of x^3 - x^2 - 10x -8 = 0

Answer 1

first guess one zero, like -1
try that -1
-1 - 1 -10(-1) - 8
-2 + 10 -8
0
ok, x = -1 works
so (x+1) is a factor
divide by long division or synthetic division
(x^3 - x^2 - 10x -8)/(x+1)
I get
x^2 - 2 x - 8
so
(x+1)(x^2 - 2 x - 8 ) = 0
get your next two roots by solving the quadratic
x^2 - 2 x - 8 = 0
I can not factor that so use the quadratic equation.

Answer 2

you can factor x^2 - 2x - 8 = 0
(x-4)(x+2)=0

therefore the three zeros [or 'roots' as I know them as] are x = 4, -1, -2