I think before you use tools like the master theorem, you should be training your intuition a little bit. In the first case, $T_1(n)$ is twice $T_1(n-1)$, plus a bit more. So as you calculate $T_1(1)$, $T_1(2)$, $T_1(3)$, and so on, each time the value is more than doubled. If you take $T_1(1000)$, that is more than $T_1(1)$ doubled 999 times, more than $2^{999}$.
Basically, anything that takes previous values only a fixed distance apart, and at least multiplies by a constant > 1, you have exponential growth.
In the second case, it's $T_2(2)$, $T_2(4)$, $T_2(8)$, $T_2(16)$ and so on where $T_2$ doubles. You have to double n to double $T_2(n)$. That by itself is just linear. You add $n^2$, so you get at least $O (n^2)$, but probably not much more. If doubling n more than doubles n, then you may have more growth. Try to find a formula yourself for the case $T(n) = 3T(n/2)$ - it's n raised to some power, so find which one.
Basically, if multiplying n by one constant > 1 multiplies T(n) by another constant > 1, you get polynomial growth - depending on the constants.