Answer
See below.
Work Step by Step
The factor theorem says that if $f(c)=0$, then $(x-c)$ is a factor of $f(x)$ and if $(x-c)$ is a factor of $f(x)$, then $f(c)=0$.
We check if $x=0.5$ is a zero:
$f(0.5)=2(0.5)^4+(0.5)^3-5(0.5)^2+10(0.5)-4=0$
Since we got $0$, we know that $0.5$ is indeed a zero of the polynomial.
