Just plug x=2 into the cubic equation to get
8-4a +34 -50 =
set it =0
4a = -8
a = -2
x-2 is a factor of x^3 +2x^2 +17x -50. the other factor is x^2 + 4x + 25
(x-2)(x^2+4x+25) = x^3 +2x^2 +17x -50
x^2 +4x + 25 has no real factors. set it equal to zero, solve for x, you get imaginary zeroes and imaginary factors.