Let the polynomial $P(x) = a_nx^n+a_{n-1}x^{n-1}+...+a_0$ has at least one real root and $a_0 \ne 0$. Prove that, consequently crossing out the monomials in the notation $P(x)$ in some order, we can obtain the number $a_0$ from it so that each intermediate polynomial also has at least one real root.