If there are infinitely many points that are not solution to the polynomial equation $F(X_1,X_2,...X_{n-1},1)=0$ then there are infinitely many points that are not solution to the polynomial equation $F(X_1,X_2,...X_{n-1},X_n)$.
Why is that?
Thank you!
P.S. I found the statement here as a solution to the problem 1.14.
First of all, $F(X_1,\dots,X_n)$ is a polynomial, not a polynomial equation. I assume that you mean $F(X_1,\dots,X_n)=0$. Then this fact is a trivial observation, since $F(X_1,\dots,X_{n-1},1)=0$ is the special case of $F(X_1,\dots, X_n)=0$ with $X_n=1$.
Does this help you? If not, please specify a little more, which part you don't understand and I will try to elaborate on this answer.