Question

P()=
X-2 is a factor of P(x)
X-2 is not a factor

Answer 1

The factor theorem says that if (x-k) is a factor of the polynomial P(x),  if and only if x=k is a zero to the equation P(x)=0.
Here
P(x)=2x^4-2x^3-6x^2+8
P(2)=2(2)^4-2(2)^3-6(2)^2+8  
=32-16-24+8
=0
So by the factor theorem, (x-2) is a factor of P(x).