3a^2+4a+5 -(2a^2+2a+3)
=3a^2+4a+5 -2a^2-2a-3
=a^2+2a+2
=a^2+2a+1+1
=(a+1)^2+1>=1
3a^2+4a+5 >2a^2+2a+3