Answer
See proof below.
Work Step by Step
1. List all possible rational zeros: $\pm1,\pm1/2,\pm2$
2. Test all values: $P(1)=2-1+1+2\ne0,P(-1)=2+1-1+2\ne0$
$P(2)=32-8+2+2\ne0,P(-2)=32_8-2+2\ne0$
$P(1/2)=1/8-1/6+1/2+2\ne0,P(-1/2)=1/8+1/8-1/2+2\ne0$
3. We conclude that there are no rational zeros.