Question

If x is an odd integer, then x

2 + 3x + 5 is odd. (Use Direct Proof)

Answer 1

Any odd number can be presented as: $x=2n+1,$ where $n$ is an integer. Thus, we get: $2+3(2n+1)+5=6n+10=2(3n+5)$. As we can see, the latter number is even. Thus, the statement is wrong.