If m, n, p are positive integers, is (m2 + n)(2m + p) odd

(1) For (m^2 + n). Since don't know if m is odd or even, don't know if m^2 is odd or even, which means adding odd, n could make whole statement odd or even. (odd + odd) = even, but (even + odd) = odd. So don't know if (m^2 + n) is odd or even.
For (2m + p). Since m is integer, 2m must even. However, don't know if p is odd or even.
So don't know if (2m + p) is odd or even.
Since don't know if (m^2 + n) is odd or even and don't know if (2m + p) is odd or even, don't know if (m^2 + n)(2m + p) is odd or even.
Insufficient
(2) For (m^2 + n). Don't know if m is odd or even, so don't know if m^2 is odd or even. Don't know if n is odd or even. So don't know if (m^2 + n) is odd or even.
For (2m + p). Since m is integer, 2m is even integer. Since p is even, (2m + p) = (even integer + even integer) = even. (2m + p) is even.
Since (m^2 + n) is integer, (m^2 + n)(2m + p) = (integer x even integer) = even integer. Always No.
Sufficient